{"id":38537,"date":"2022-11-16T01:12:48","date_gmt":"2022-11-15T19:42:48","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=38537"},"modified":"2022-11-17T01:53:08","modified_gmt":"2022-11-16T20:23:08","slug":"big-ideas-math-algebra-2-answers-chapter-8","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/big-ideas-math-algebra-2-answers-chapter-8\/","title":{"rendered":"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series"},"content":{"rendered":"<p>Hey guys!!! Are you looking for the best guide to solve the Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series Questions? If our guess is correct, then you are on the right page. Here the students can get <a href=\"https:\/\/ccssanswers.com\/big-ideas-math-algebra-2-answers\/\">Big Ideas Math Algebra 2 Answers<\/a> Ch 8 Sequences and Series with brief explanations. So, the students who are confused about the concept of sequences and series can make use of this Big Ideas Math Book Algebra 2 Ch 8 Sequences and Series. Get access to the user-friendly solutions provided for all the concepts of Chapter 8 Sequences and Series from Big Ideas Math Algebra 2 Textbooks from here.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 2 Answer Key Chapter 8 Sequences and Series<\/h2>\n<p>A sequence is an arrangement of numbers in a specific order whereas a series is defined as the sum of elements in a sequence. Enhance your performance in the final exams by practicing the Big Ideas Math Algebra 2 Answers Ch 8 Sequences and Series on a daily basis. BIM Algebra 2 Chapter 8 Sequences and Series Answer Key aligned as per the Big Ideas Math Textbooks Latest Common Core Curriculum. Tap the below links to learn the concepts of BIM Algebra 2 Chapter 8 Sequences and Series easily and quickly. The Question and Answers include Exercises, Chapter Tests, Review Tests, Cumulative Practice, Cumulative Assessments, Exercise Questions, and so on.<\/p>\n<ul>\n<li><a href=\"#Sequences_and_Series_Maintaining_Mathematical_Proficiency\">Sequences and Series Maintaining Mathematical Proficiency &#8211; Page 407<\/a><\/li>\n<li><a href=\"#Sequences_and_Series_Mathematical_Practices\">Sequences and Series Mathematical Practices &#8211; Page 408<\/a><\/li>\n<li><a href=\"#Lesson_8.1_Defining_and_Using_Sequences_and_Series\">Lesson 8.1 Defining and Using Sequences and Series &#8211; Page(409-416)<\/a><\/li>\n<li><a href=\"#Defining_and_Using_Sequences_and_Series_8.1_Exercises\">Defining and Using Sequences and Series 8.1 Exercises &#8211; Page(414-416)<\/a><\/li>\n<li><a href=\"#Lesson_8.2_Analyzing_Arithmetic_Sequences_and_Series\">Lesson 8.2 Analyzing Arithmetic Sequences and Series &#8211; Page(417-424)<\/a><\/li>\n<li><a href=\"#Analyzing_Arithmetic_Sequences_and_Series_8.2_Exercises\">Analyzing Arithmetic Sequences and Series 8.2 Exercises &#8211; Page(422-424)<\/a><\/li>\n<li><a href=\"#Lesson_8.3_Analyzing_Geometric_Sequences_and_Series\">Lesson 8.3 Analyzing Geometric Sequences and Series &#8211; Page(425-432)<\/a><\/li>\n<li><a href=\"#Analyzing_Geometric_Sequences_and_Series_8.3_Exercises\">Analyzing Geometric Sequences and Series 8.3 Exercises &#8211; Page(430-432)<\/a><\/li>\n<li><a href=\"#Sequences_and_Series_Study_Skills:_Keeping_Your_Mind_Focused\">Sequences and Series Study Skills: Keeping Your Mind Focused &#8211; Page 433<\/a><\/li>\n<li><a href=\"#Sequences_and_Series_8.1_\u2013_8.3_Quiz\">Sequences and Series 8.1 \u2013 8.3 Quiz &#8211; Page 434<\/a><\/li>\n<li><a href=\"#Lesson_8.4_Finding_Sums_of_Infinite_Geometric_Series\">Lesson 8.4 Finding Sums of Infinite Geometric Series &#8211; Page(435-440)<\/a><\/li>\n<li><a href=\"#Finding_Sums_of_Infinite_Geometric_Series_8.4_Exercises\">Finding Sums of Infinite Geometric Series 8.4 Exercises &#8211; Page(439-440)<\/a><\/li>\n<li><a href=\"#Lesson_8.5_Using_Recursive_Rules_with_Sequences\">Lesson 8.5 Using Recursive Rules with Sequences &#8211; Page(441-450)<\/a><\/li>\n<li><a href=\"#Using_Recursive_Rules_with_Sequences_8.5_Exercises\">Using Recursive Rules with Sequences 8.5 Exercises &#8211; Page(447-450)<\/a><\/li>\n<li><a href=\"#Sequences_and_Series_Performance_Task:_Integrated_Circuits_and_Moore_s_Law\">Sequences and Series Performance Task: Integrated Circuits and Moore s Law &#8211; Page 451<\/a><\/li>\n<li><a href=\"#Sequences_and_Series_Chapter_Review\">Sequences and Series Chapter Review &#8211; Page(452-454)\u00a0<\/a><\/li>\n<li><a href=\"#Sequences_and_Series_Chapter_Test\">Sequences and Series Chapter Test &#8211; Page 455<\/a><\/li>\n<li><a href=\"#Sequences_and_Series_Cumulative_Assessment\">Sequences and Series Cumulative Assessment &#8211; Page(456-457)\u00a0<\/a><\/li>\n<\/ul>\n<h3><a id=\"Sequences_and_Series_Maintaining_Mathematical_Proficiency\"><\/a>Sequences and Series Maintaining Mathematical Proficiency<\/h3>\n<p><strong>Copy and complete the table to evaluate the function.<\/strong><br \/>\nQuestion 1.<br \/>\ny = 3 \u2212 2<sup>x<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38629\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-1.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 1.1\" width=\"167\" height=\"138\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-113909\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer1.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer1.jpg\" width=\"205\" height=\"293\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer1.jpg 357w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer1-210x300.jpg 210w\" sizes=\"(max-width: 205px) 100vw, 205px\" \/><\/p>\n<p>Question 2.<br \/>\ny = 5x<sup>2<\/sup> + 1<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38630\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-1.2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 1.2\" width=\"159\" height=\"135\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-113912\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-2.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-2.jpg\" width=\"286\" height=\"577\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-2.jpg 376w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-2-149x300.jpg 149w\" sizes=\"(max-width: 286px) 100vw, 286px\" \/><\/p>\n<p>Question 3.<br \/>\ny = \u22124x + 24<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38631\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-1.3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 1.3\" width=\"163\" height=\"136\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-113924\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-3-1.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-3-1.jpg\" width=\"220\" height=\"399\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-3-1.jpg 282w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-3-1-165x300.jpg 165w\" sizes=\"(max-width: 220px) 100vw, 220px\" \/><\/p>\n<p><strong>Solve the equation. Check your solution(s).<\/strong><br \/>\nQuestion 4.<br \/>\n7x + 3 = 31<br \/>\nAnswer:<br \/>\nGiven,<br \/>\n7x + 3 = 31<br \/>\nSubtract 3 on both sides<br \/>\n7x + 3 &#8211; 3 = 31 &#8211; 3<br \/>\n7x = 28<br \/>\nx = 28\/7<br \/>\nx = 4<br \/>\nSo, the solution is x = 4.<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{1}{16}\\) = 4 (\\(\\frac{1}{2}\\)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113934\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-5.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-5.jpg\" width=\"151\" height=\"196\" \/><br \/>\nQuestion 6.<br \/>\n216 = 3(x + 6)<br \/>\nAnswer:<br \/>\nGiven,<br \/>\n216 = 3(x + 6)<br \/>\n216 = 3(x) + 3(6)<br \/>\n216 = 3x + 18<br \/>\nSubtract 18 on both sides<br \/>\n3x + 18 &#8211; 18 = 216 &#8211; 18<br \/>\n3x = 198<br \/>\nx = 198\/3<br \/>\nx = 66<br \/>\nSo, the solution is x = 66.<\/p>\n<p>Question 7.<br \/>\n2<sup>x<\/sup> + 16 = 144<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-113842\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-7JPG.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-7JPG.jpg\" width=\"185\" height=\"123\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\frac{1}{4}\\)x \u2212 8 = 17<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113935\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-8.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-8.jpg\" width=\"142\" height=\"191\" \/><br \/>\nQuestion 9.<br \/>\n8(\\(\\frac{3}{4}\\))<sup>x<\/sup> = \\(\\frac{27}{8}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-113936\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-9.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Answer-9.jpg\" width=\"126\" height=\"144\" \/><br \/>\nQuestion 10.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nThe graph of the exponential decay function f(x) = bx has an asymptote y = 0. How is the graph of f different from a scatter plot consisting of the points (1, b<sup>1<\/sup>), (2, b<sup>21<\/sup> + b<sup>2<\/sup>), (3, b<sup>1<\/sup> + b<sup>2<\/sup> + b<sup>3<\/sup>), . . .? How is the graph of f similar?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Sequences_and_Series_Mathematical_Practices\"><\/a>Sequences and Series Mathematical Practices<\/h3>\n<p>Mathematically proficient students consider the available tools when solving a mathematical problem.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Use a spreadsheet to help you answer the question.<\/strong><br \/>\nQuestion 1.<br \/>\nA pilot flies a plane at a speed of 500 miles per hour for 4 hours. Find the total distance flown at 30-minute intervals. Describe the pattern.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nA population of 60 rabbits increases by 25% each year for 8 years. Find the population at the end of each year. Describe the type of growth.<br \/>\nAnswer:<br \/>\nA population of 60 rabbits increases by 25% each year for 8 years.<br \/>\nThe population at the end of the year = P + P \u00d7 (rate of increase)\/100<br \/>\nYear 1 of 8: 60 + 60 \u00d7 25\/100 = 60 + 15 = 75<br \/>\nYear 2 of 8: 75 + 75 \u00d7 0.25 = 75 + 18.75 = 93.75 = 94<br \/>\nYear 3 of 8: 93.75 + 93.75 \u00d7 0.25 = 117<br \/>\nYear 4 of 8: 117 + 117 \u00d7 0.25 = 146<br \/>\nYear 5 of 8: 146 + 146 \u00d7 0.25 = 183<br \/>\nYear 6 of 8: 183 + 183 \u00d7 0.25 = 228<br \/>\nYear 7 of 8: 228 + 228 \u00d7 0.25 = 286<br \/>\nYear 8 of 8 (Final year): 286 + 286 \u00d7 0.25 = 357<br \/>\nThe type of growth is exponential.<\/p>\n<p>Question 3.<br \/>\nAn endangered population has 500 members. The population declines by 10% each decade for 80 years. Find the population at the end of each decade. Describe the type of decline.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nThe top eight runners finishing a race receive cash prizes. First place receives $200, second place receives $175, third place receives $150, and so on. Find the fifth through eighth place prizes. Describe the type of decline.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_8.1_Defining_and_Using_Sequences_and_Series\"><\/a>Lesson 8.1 Defining and Using Sequences and Series<\/h3>\n<p><strong>Essential Question<\/strong> How can you write a rule for the nth term of a sequence?<br \/>\nA sequence is an ordered list of numbers. There can be a limited number or an infinite number of terms of a sequence.<br \/>\na<sub>1<\/sub>, a<sub>2<\/sub>, a<sub>3<\/sub>, a<sub>4<\/sub>, . . . , a<sub>n<\/sub>, . . .Terms of a sequence<br \/>\nHere is an example. 1, 4, 7, 10, . . . , 3<sub>n-2<\/sub>, . . .<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing Rules for Sequences<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38632\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 1\" width=\"222\" height=\"137\" \/><br \/>\nWork with a partner. Match each sequence with its graph. The horizontal axes represent n, the position of each term in the sequence. Then write a rule for the nth term of the sequence, and use the rule to find a<sub>10<\/sub>.<br \/>\na. 1, 2.5, 4, 5.5, 7, . . .<br \/>\nb. 8, 6.5, 5, 3.5, 2, . . .<br \/>\nc. \\(\\frac{1}{4}, \\frac{4}{4}, \\frac{9}{4}, \\frac{16}{4}, \\frac{25}{4}, \\ldots\\)<br \/>\nd. \\(\\frac{25}{4}, \\frac{16}{4}, \\frac{9}{4}, \\frac{4}{4}, \\frac{1}{4}, \\ldots\\)<br \/>\ne. \\(\\frac{1}{2}\\), 1, 2, 4, 8, . . .<br \/>\nf. 8, 4, 2, 1, \\(\\frac{1}{2}\\), . . .<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38633\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 2\" width=\"481\" height=\"415\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-2.png 481w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-2-300x259.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 2.<br \/>\nHow can you write a rule for the nth term of a sequence?<br \/>\nAnswer:<br \/>\nThe nth term of a sequence (arithmetic)<br \/>\na<sub>n<\/sub> = a<sub>1<\/sub> + (n-1)(d)<br \/>\nd = common difference<br \/>\na1 = first term<\/p>\n<p>Question 3.<br \/>\nWhat do you notice about the relationship between the terms in (a) an arithmetic sequence and (b) a geometric sequence? Justify your<br \/>\nAnswer:<br \/>\nAn arithmetic sequence is a set of numbers in which a term has a fixed amount with the previous term. A geometric sequence is a series of integers in which each element after the first is obtained by multiplying the preceding number by a constant factor.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Write the first six terms of the sequence.<\/strong><br \/>\nQuestion 1.<br \/>\na<sub>n<\/sub> = n + 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-111874\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-1.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-1.jpg\" width=\"453\" height=\"157\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-1.jpg 453w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-1-300x104.jpg 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Question 2.<br \/>\nf(n) = (\u22122)<sup>n-1<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-111875\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-2.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-2.jpg\" width=\"491\" height=\"201\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-2.jpg 491w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-2-300x123.jpg 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Question 3.<br \/>\na<sub>n<\/sub> = \\(\\frac{n}{n+1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-111876\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-3.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-3.jpg\" width=\"440\" height=\"312\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-3.jpg 440w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-3-300x213.jpg 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p><strong>Describe the pattern, write the next term, graph the first five terms, and write a rule for the nth term of the sequence.<\/strong><br \/>\nQuestion 4.<br \/>\n3, 5, 7, 9, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-111877\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-4.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-4.jpg\" width=\"422\" height=\"600\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-4.jpg 422w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-4-211x300.jpg 211w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Question 5.<br \/>\n3, 8, 15, 24, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-111878\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-5.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-5.jpg\" width=\"513\" height=\"582\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-5.jpg 513w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-5-264x300.jpg 264w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 6.<br \/>\n1, \u22122, 4, \u22128, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-111879\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-6.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-6.jpg\" width=\"398\" height=\"537\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-6.jpg 398w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.1-Answer-6-222x300.jpg 222w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p>\n<p>Question 7.<br \/>\n2, 5, 10, 17, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113620\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-7.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-7.jpg\" width=\"468\" height=\"567\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-7.jpg 468w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-7-248x300.jpg 248w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 8.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 3, suppose there are nine layers of apples. How many apples are in the ninth layer?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113621\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-8.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-8.jpg\" width=\"378\" height=\"309\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-8.jpg 378w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-8-300x245.jpg 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p><strong>Write the series using summation notation.<\/strong><br \/>\nQuestion 9.<br \/>\n5 + 10 + 15 +. . .+ 100<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113622\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-9.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-9.jpg\" width=\"427\" height=\"152\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-9.jpg 427w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-9-300x107.jpg 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\frac{1}{2}+\\frac{4}{5}+\\frac{9}{10}+\\frac{16}{17}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113623\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-10.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-10.jpg\" width=\"408\" height=\"287\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-10.jpg 408w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-10-300x211.jpg 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p>Question 11.<br \/>\n6 + 36 + 216 + 1296 + . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113624\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-11.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-11.jpg\" width=\"448\" height=\"151\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-11.jpg 448w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-11-300x101.jpg 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><\/p>\n<p>Question 12.<br \/>\n5 + 6 + 7 +. . .+ 12<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113625\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-12.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-12.jpg\" width=\"443\" height=\"149\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-12.jpg 443w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-12-300x101.jpg 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p><strong>Find the sum.<\/strong><br \/>\nQuestion 13.<br \/>\n\\(\\sum_{i=1}^{5}\\) 8i<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113626\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-13.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-13.jpg\" width=\"455\" height=\"176\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-13.jpg 455w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-13-300x116.jpg 300w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><\/p>\n<p>Question 14.<br \/>\n\\(\\sum_{k=3}^{7}\\)(k<sup>2<\/sup> \u2212 1)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/25\/d837c0729a1d7b18fdec84e2d36a823a\/d29c97a7737acd94701521110af95ab0\/lateximg.png?tcb=1622090466\" \/><\/p>\n<p>Question 15.<br \/>\n\\(\\sum_{i=1}^{34}\\)1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113627\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-15.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-15.jpg\" width=\"329\" height=\"89\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-15.jpg 329w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-15-300x81.jpg 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p>Question 16.<br \/>\n\\(\\sum_{k=1}^{6}\\)k<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113629\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-16.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-16.jpg\" width=\"407\" height=\"150\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-16.jpg 407w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.1-Answer-16-300x111.jpg 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>Question 17.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nSuppose there are nine layers in the apple stack in Example 3. How many apples are in the stack?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/25\/bac8dd73d4e787c9506d6ddbd8f83d62\/d66527e527ad7709124fa1ebbeeb0fa7\/lateximg.png?tcb=1621704211\" \/><\/p>\n<h3><a id=\"Defining_and_Using_Sequences_and_Series_8.1_Exercises\"><\/a>Defining and Using Sequences and Series 8.1 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is another name for summation notation?<br \/>\nAnswer: The another name for summation notation is sigma notation.<\/p>\n<p>Question 2.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nIn a sequence, the numbers are called __________ of the sequence.<br \/>\nAnswer:<br \/>\nIn a sequence, the numbers are called the <span style=\"text-decoration: underline;\"><strong>terms<\/strong> <\/span>of the sequence.<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare sequences and series.<br \/>\nAnswer: A sequence is a specific list of numbers and a series is the sum of terms of a sequence.<\/p>\n<p>Question 4.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich does not belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38634\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 3\" width=\"502\" height=\"64\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-3.png 502w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-3-300x38.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/25\/b75a58ec37e9d1fbf49b503e4b00af69\/333ae80e9f402f7401f50f7b40dd0946\/lateximg.png?tcb=1621778973\" \/><\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201314, write the first six terms of the sequence.<\/strong><br \/>\nQuestion 5.<br \/>\na<sub>n<\/sub> = n + 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/c04ff8597bec93e9b82240edb9f262a1\/c5129576dfc44022ff77e69b9dbc90fd\/lateximg.png?tcb=1621779025\" \/><\/p>\n<p>Question 6.<br \/>\na<sub>n<\/sub> = 6 \u2212 n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/cf8fc60cb6902e5d9d9c9958aab9107f\/b24734159311d4c1ee3dc28b24d4136f\/lateximg.png?tcb=1621779046\" \/><\/p>\n<p>Question 7.<br \/>\na<sub>n<\/sub> = n<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45641\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 7\" width=\"147\" height=\"210\" \/><\/p>\n<p>Question 8.<br \/>\nf(n) = n<sup>3<\/sup> + 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/f5d9d10382c9bc79043222a6c36400a4\/7b4712314241ac40c3cafa63ec59a6b6\/lateximg.png?tcb=1621779067\" \/><\/p>\n<p>Question 9.<br \/>\nf(n) = 4<sup>n-1<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45642\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 9\" width=\"201\" height=\"209\" \/><\/p>\n<p>Question 10.<br \/>\na<sub>n<\/sub> = \u2212n<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/cdda38dcce83af766be36c1a230808f5\/8d5f386c8f0935f9ec7061d4582b4f91\/lateximg.png?tcb=1621779132\" \/><img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/cdda38dcce83af766be36c1a230808f5\/8d5f386c8f0935f9ec7061d4582b4f91\/lateximg.png?tcb=1621779132\" \/><\/p>\n<p>Question 11.<br \/>\na<sub>n<\/sub> = n<sup>2<\/sup> \u2212 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45643\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 11\" width=\"176\" height=\"210\" \/><\/p>\n<p>Question 12.<br \/>\na<sub>n<\/sub> = (n + 3)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/02\/27\/4e2f0481b664dd0d2a7f3996eaf80321\/412a9d510df273e460acb08ec685313c\/lateximg.png?tcb=1621779172\" \/><\/p>\n<p>Question 13.<br \/>\nf(n) = \\(\\frac{2n}{n+2}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45644\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 13\" width=\"191\" height=\"351\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-13.png 191w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-13-163x300.png 163w\" sizes=\"(max-width: 191px) 100vw, 191px\" \/><\/p>\n<p>Question 14.<br \/>\nf(n) = \\(\\frac{n}{2n-1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/bdbbc5627906edcaab469ab263b99889\/f58f1981a48e72af1a298475b951d625\/lateximg.png?tcb=1621779204\" \/><\/p>\n<p><strong>In Exercises 15\u201326, describe the pattern, write the next term, and write a rule for the nth term of the sequence.<\/strong><br \/>\nQuestion 15.<br \/>\n1, 6, 11, 16, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45645\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 15\" width=\"530\" height=\"118\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-15.png 530w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-15-300x67.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 16.<br \/>\n1, 2, 4, 8, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/1a44cfe85846191fb2ede122be1537ba\/04a0c273e4492897585e41b5b09bfe09\/lateximg.png?tcb=1621779240\" \/><\/p>\n<p>Question 17.<br \/>\n3.1, 3.8, 4.5, 5.2, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45646\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 17\" width=\"492\" height=\"122\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-17.png 492w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-17-300x74.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/p>\n<p>Question 18.<br \/>\n9, 16.8, 24.6, 32.4, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/65bca792a78ca1f533f50e44a435f594\/3b329c46bb5fcd783c6dc1efc581ff3f\/lateximg.png?tcb=1621779265\" \/><\/p>\n<p>Question 19.<br \/>\n5.8, 4.2, 2.6, 1, \u22120.6 . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45647\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 19\" width=\"542\" height=\"119\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-19.png 542w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-19-300x66.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 20.<br \/>\n\u22124, 8, \u221212, 16, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/c7739763b68bf1bd732b542f6809b7cf\/bbdeb3dd4c06a6557be01c7c47c9648e\/lateximg.png?tcb=1621779374\" \/><\/p>\n<p>Question 21.<br \/>\n\\(\\frac{1}{4}, \\frac{2}{4}, \\frac{3}{4}, \\frac{4}{4}, \\ldots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45648\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 21\" width=\"519\" height=\"115\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-21.png 519w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-21-300x66.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 22.<br \/>\n\\(\\frac{1}{10}, \\frac{3}{20}, \\frac{5}{30}, \\frac{7}{40}, \\ldots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/6dfc1ad34bdd3d6417633ceff691ba58\/58e16cc1aafa569045ea0360d79ee199\/lateximg.png?tcb=1621779447\" \/><\/p>\n<p>Question 23.<br \/>\n\\(\\frac{2}{3}, \\frac{2}{6}, \\frac{2}{9}, \\frac{2}{12}, \\ldots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45649\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 23\" width=\"495\" height=\"167\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-23.png 495w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-23-300x101.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\frac{2}{3}, \\frac{4}{4}, \\frac{6}{5}, \\frac{8}{6}, \\ldots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/00e06aaf46f3392140ad4447c15521c7\/14f4d3cb7ff11e9488cd7d4d97fa72ec\/lateximg.png?tcb=1621779488\" \/><\/p>\n<p>Question 25.<br \/>\n2, 9, 28, 65, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45650\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 25\" width=\"559\" height=\"90\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-25.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-25-300x48.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 26.<br \/>\n1.2, 4.2, 9.2, 16.2, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/02\/e15669e1ab8686fedeaba481a8a75a4f\/1c221ad7a9f4454fdc2b0cd0f02159a6\/lateximg.png?tcb=1621779534\" \/><\/p>\n<p>Question 27.<br \/>\n<strong>FINDING A PATTERN<\/strong><br \/>\nWhich rule gives the total number of squares in the nth figure of the pattern shown? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38635\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-4.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 4\" width=\"293\" height=\"192\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45651\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 27\" width=\"587\" height=\"118\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-27.png 587w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-27-300x60.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>FINDING A PATTERN<\/strong><br \/>\nWhich rule gives the total number of green squares in the nth figure of the pattern shown? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38636\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 5\" width=\"291\" height=\"196\" \/><br \/>\nAnswer:<br \/>\nA. an = n\u00b2 &#8211; 1<br \/>\nn = 1<br \/>\na1 = 1 &#8211; 1 = 0<br \/>\nn = 2<br \/>\na2 = 2\u00b2 &#8211; 1 = 4 &#8211; 1 = 3<br \/>\nn = 3<br \/>\na3 = 3\u00b2 &#8211; 1 = 9 &#8211; 1 = 8<br \/>\nn = 4<br \/>\na4 = 4\u00b2 &#8211; 1 = 16 &#8211; 1 = 15<br \/>\nB. an = n\u00b2\/2<br \/>\nn = 1<br \/>\na1 = 1\u00b2\/2 = 1\/2<br \/>\nn = 2<br \/>\na2 = 2\u00b2\/2 = 4\/2 = 2<br \/>\nn = 3<br \/>\na3 = 3\u00b2\/2 = 9\/2<br \/>\nn = 4<br \/>\na4 = 4\u00b2\/2 = 16\/2 = 8<br \/>\nC. an = 4n<br \/>\nn = 1<br \/>\na1 = 4(1) = 4<br \/>\nn = 2<br \/>\na2 = 4(2) = 8<br \/>\nn = 3<br \/>\na3 = 4(3) = 12<br \/>\nn = 4<br \/>\na4 = 4(4) = 16<br \/>\nD. an = 2n + 1<br \/>\nn = 1<br \/>\na1 = 2(1) + 1 = 3<br \/>\nn = 2<br \/>\na2 = 2(2) + 1 = 5<br \/>\nn = 3<br \/>\na3 = 2(3) + 1 = 7<br \/>\nn = 4<br \/>\na4 = 2(4) + 1 = 9<br \/>\nOption C is the correct answer.<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nRectangular tables are placed together along their short edges, as shown in the diagram. Write a rule for the number of people that can be seated around n tables arranged in this manner. Then graph the sequence.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38637\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-6.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 6\" width=\"295\" height=\"178\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45652\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 29\" width=\"625\" height=\"541\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-29.png 625w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-29-300x260.png 300w\" sizes=\"(max-width: 625px) 100vw, 625px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nAn employee at a construction company earns $33,000 for the first year of employment. Employees at the company receive raises of $2400 each year. Write a rule for the salary of the employee each year. Then graph the sequence.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/25\/dd2e0577dbb096a5e4d9d326d4584d3f\/72cde0adb4deee5dbc73e761fb3ee9d6\/lateximg.png?tcb=1621781402\" \/><\/p>\n<p><strong>In Exercises 31\u201338, write the series using summation notation.<\/strong><br \/>\nQuestion 31.<br \/>\n7 + 10 + 13 + 16 + 19<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45653\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 31\" width=\"560\" height=\"182\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-31.png 560w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-31-300x98.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 32.<br \/>\n5 + 11 + 17 + 23 + 29<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-112034\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-32.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-32.jpg\" width=\"489\" height=\"189\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-32.jpg 383w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-32-300x116.jpg 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><\/p>\n<p>Question 33.<br \/>\n4 + 7 + 12 + 19 + . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45654\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 33\" width=\"559\" height=\"197\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-33.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-33-300x106.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 34.<br \/>\n-1 + 2 + 7 + 14 + &#8230;..<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/25\/cf1a7aeb80aa8c801bc9475f634b8955\/c9d751e4565c262a2c6f25f2641fdcb0\/lateximg.png?tcb=1621781953\" width=\"538\" height=\"243\" \/><\/p>\n<p>Question 35.<br \/>\n\\(\\frac{1}{3}+\\frac{1}{9}+\\frac{1}{27}+\\frac{1}{81}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45655\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 35\" width=\"525\" height=\"248\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-35.png 525w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-35-300x142.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 36.<br \/>\n\\(\\frac{1}{4}+\\frac{2}{5}+\\frac{3}{6}+\\frac{4}{7}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/25\/0ee4d0848038b540d8e4a0c1bcb1ba61\/d8ed9cbad39fa88a49286f8c2499ee91\/lateximg.png?tcb=1621781993\" width=\"532\" height=\"217\" \/><\/p>\n<p>Question 37.<br \/>\n\u22123 + 4 \u2212 5 + 6 \u2212 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112035\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-37.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-37.jpg\" width=\"218\" height=\"148\" \/><br \/>\nQuestion 38.<br \/>\n\u22122 + 4 \u2212 8 + 16 \u2212 32<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112519\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-38JPG..jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-38JPG..jpg\" width=\"273\" height=\"124\" \/><\/p>\n<p><strong>In Exercises 39\u201350, find the sum.<\/strong><br \/>\nQuestion 39.<br \/>\n\\(\\sum_{i=1}^{6}\\)2i<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45657\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 39\" width=\"474\" height=\"255\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-39.png 474w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-39-300x161.png 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>Question 40.<br \/>\n\\(\\sum_{i=1}^{5}\\)7i<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/25\/de83293e4785ec0573d0ae5e966ff77d\/f43eff0d42d11cd94e41feaf30f26faf\/lateximg.png?tcb=1621920805\" \/><\/p>\n<p>Question 41.<br \/>\n\\(\\sum_{n=0}^{4}\\)n<sup>3<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45658\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 41\" width=\"313\" height=\"116\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-41.png 313w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-41-300x111.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><\/p>\n<p>Question 42.<br \/>\n\\(\\sum_{k=1}^{4}\\)3k<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/25\/baccfb35155ddffded1aeddbd8a84dd9\/6aff941702c9038d26bf66cae80fe241\/lateximg.png?tcb=1621920836\" \/><\/p>\n<p>Question 43.<br \/>\n\\(\\sum_{k=3}^{6}\\)(5k \u2212 2)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45659\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-43.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 43\" width=\"547\" height=\"143\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-43.png 547w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-43-300x78.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 44.<br \/>\n\\(\\sum_{n=1}^{5}\\)(n<sup>2<\/sup> \u2212 1)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/09\/b62926adf5337a9749787d26f0822d2f\/a71a6e72b5bc7ab2b036b376d98424a2\/lateximg.png?tcb=1621920871\" \/><\/p>\n<p>Question 45.<br \/>\n\\(\\sum_{i=2}^{8} \\frac{2}{i}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45660\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-45.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 45\" width=\"556\" height=\"287\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-45.png 556w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-45-300x155.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 46.<br \/>\n\\(\\sum_{k=4}^{6} \\frac{k}{k+1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/09\/859b0e241d17d978875dc7c0004b46d1\/7d5bddf7cab670756842e2231b8ca5fc\/lateximg.png?tcb=1621920891\" \/><\/p>\n<p>Question 47.<br \/>\n\\(\\sum_{i=1}^{35}\\)1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45661\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-47.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 47\" width=\"146\" height=\"64\" \/><\/p>\n<p>Question 48.<br \/>\n\\(\\sum_{n=1}^{16}\\)n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/16\/04\/06\/2542741a5e680974f2d10fbfd8993171\/565c3b2efb4779d3441489d4468853f4\/lateximg.png?tcb=1621920909\" \/><\/p>\n<p>Question 49.<br \/>\n\\(\\sum_{i=10}^{25}\\)i<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45662\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-49.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 49\" width=\"547\" height=\"281\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-49.png 547w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-49-300x154.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 50.<br \/>\n\\(\\sum_{n=1}^{18}\\)n<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/26\/33114d316347749f3e9f43de339a6712\/764eb6d1138c6ba57609ad86ea34c69b\/lateximg.png?tcb=1621920955\" \/><\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 51 and 52, describe and correct the error in finding the sum of the series.<br \/>\nQuestion 51.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38638\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 7\" width=\"318\" height=\"107\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-7.png 318w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-7-300x101.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45663\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-51.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 51\" width=\"560\" height=\"186\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-51.png 560w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-51-300x100.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 52.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38639\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-8.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 8\" width=\"266\" height=\"120\" \/><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou want to save $500 for a school trip. You begin by saving a penny on the first day. You save an additional penny each day after that. For example, you will save two pennies on the second day, three pennies on the third day, and so on.<br \/>\na. How much money will you have saved after 100 days?<br \/>\nb. Use a series to determine how many days it takes you to save $500.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45664\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-53.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 53\" width=\"575\" height=\"658\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-53.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-53-262x300.png 262w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou begin an exercise program. The first week you do 25 push-ups. Each week you do 10 more push-ups than the previous week. How many push-ups will you do in the ninth week? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38640\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 9\" width=\"149\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-112520\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-54JPG.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-54JPG.jpg\" width=\"429\" height=\"284\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-54JPG.jpg 414w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.1-Answer-54JPG-300x199.jpg 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><\/p>\n<p>Question 55.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nFor a display at a sports store, you are stacking soccer balls in a pyramid whose base is an equilateral triangle with five layers. Write a rule for the number of soccer balls in each layer. Then graph the sequence.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38641\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-10.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 10\" width=\"268\" height=\"220\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45665\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-55.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 55\" width=\"548\" height=\"379\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-55.png 548w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-55-300x207.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the diagram to determine the sum of the series. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38642\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-11.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 11\" width=\"242\" height=\"188\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/26\/f61d963baa9d191449ca8bcd4e2c9ff6\/20334d5bc41ff2f5f27b1c3493b12271\/lateximg.png?tcb=1621921069\" \/><\/p>\n<p>Question 57.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYou use a calculator to evaluate \\(\\sum_{i=3}^{1659}\\)i because the lower limit of summation is 3, not 1. Your friend claims there is a way to use the formula for the sum of the first n positive integers. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45666\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-57.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 57\" width=\"545\" height=\"244\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-57.png 545w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-57-300x134.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nA regular polygon has equal angle measures and equal side lengths. For a regular n-sided polygon (n \u2265 3), the measure an of an interior angle is given by a<sub>n<\/sub> = \\(\\frac{180(n-2)}{n}\\)<br \/>\na. Write the first five terms of the sequence.<br \/>\nAnswer:<br \/>\nn = 3<br \/>\nan = 180(n &#8211; 2)\/n<br \/>\nan = 180(3 &#8211; 2)\/3<br \/>\nan = 180\/3 = 60<br \/>\nan = 60<br \/>\nn = 4<br \/>\nan = 180(n &#8211; 2)\/n<br \/>\nan = 180(4 &#8211; 2)\/4<br \/>\nan = 180\/3 = 60<br \/>\nan = 45 \u00d7 2<br \/>\nan = 90<br \/>\nThe value of each interior angle of a 4-sided polygon is 90 degrees.<br \/>\nn = 5<br \/>\nan = 180(n &#8211; 2)\/n<br \/>\nan = 180(5 &#8211; 2)\/5<br \/>\nan = 36 \u00d7 3<br \/>\nan = 108<br \/>\nThe value of each interior angle of a 5-sided polygon is 108 degrees.n = 6<br \/>\nan = 180(n &#8211; 2)\/n<br \/>\nan = 180(6 &#8211; 2)\/6<br \/>\nan = 30 \u00d7 4<br \/>\nan = 120<br \/>\nThe value of each interior angle of a 6-sided polygon is 120 degrees.<br \/>\nn = 7<br \/>\nan = 180(n &#8211; 2)\/n<br \/>\nan = 180(7 &#8211; 2)\/7<br \/>\nan = 25.71 \u00d7 5<br \/>\nan = 128.55<br \/>\nThe value of each interior angle of a 7-sided polygon is 128.55 degrees.<\/p>\n<p>b. Write a rule for the sequence giving the sum Tn of the measures of the interior angles in each regular n-sided polygon.<br \/>\nAnswer: Tn = 180(n &#8211; 2)<\/p>\n<p>c. Use your rule in part (b) to find the sum of the interior angle measures in the Guggenheim Museum skylight, which is a regular dodecagon.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38643\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-12.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 12\" width=\"270\" height=\"204\" \/><br \/>\nAnswer:<br \/>\nn = 12<br \/>\nTn = 180(n &#8211; 2)<br \/>\nTn = 180(12 &#8211; 2)<br \/>\nTn = 180 \u00d7 10<br \/>\nTn = 1800\u00b0<\/p>\n<p>Question 59.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nDetermine whether each statement is true. If so, provide a proof. If not, provide a counterexample.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45667\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-59.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 59.1\" width=\"549\" height=\"520\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-59.1.png 549w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-59.1-300x284.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45668\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-59.2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 59.2\" width=\"311\" height=\"372\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-59.2.png 311w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-59.2-251x300.png 251w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nIn this section, you learned the following formulas.<br \/>\n\\(\\sum_{i=1}^{n}\\)1 = n<br \/>\n\\(\\sum_{i=1}^{n}\\)i = \\(\\frac{n(n+1)}{2}\\)<br \/>\n\\(\\sum_{i=1}^{n}\\)i<sup>2<\/sup> = \\(\\frac{n(n+1)(2 n+1)}{6}\\)<br \/>\nWrite a formula for the sum of the cubes of the first n positive integers.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/09\/b8d63767a9d24e2d5ca8d0510d7f4d45\/3c878740808558aefc58559a49982c43\/lateximg.png?tcb=1621921099\" width=\"221\" height=\"50\" \/><\/p>\n<p>Question 61.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn the puzzle called the Tower of Hanoi, the object is to use a series of moves to take the rings from one peg and stack them in order on another peg. A move consists of moving exactly one ring, and no ring may be placed on top of a smaller ring. The minimum number an of moves required to move n rings is 1 for 1 ring, 3 for 2 rings, 7 for 3 rings, 15 for 4 rings, and 31 for 5 rings.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38645\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-14.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 14\" width=\"338\" height=\"110\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-14.png 338w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-14-300x98.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><br \/>\na. Write a rule for the sequence.<br \/>\nb. What is the minimum number of moves required to move 6 rings? 7 rings? 8 rings?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45669\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-61.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 61\" width=\"585\" height=\"311\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-61.png 585w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-61-300x159.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the system. Check your solution.<\/strong><br \/>\nQuestion 62.<br \/>\n2x \u2212y \u2212 3z = 6<br \/>\nx + y + 4z =\u22121<br \/>\n3x \u2212 2z = 8<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/09\/5d002cc02abaff6440424143c2c02a2a\/fc466a1a242d034e81bcba328567f461\/lateximg.png?tcb=1621921120\" \/><\/p>\n<p>Question 63.<br \/>\n2x \u2212 2y + z = 5<br \/>\n\u22122x + 3y + 2z = \u22121<br \/>\nx \u2212 4y + 5z = 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45670\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-63.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 63.1\" width=\"215\" height=\"617\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-63.1.png 215w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-63.1-105x300.png 105w\" sizes=\"(max-width: 215px) 100vw, 215px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45671\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-63.2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series 8.1 a 63.2\" width=\"371\" height=\"168\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-63.2.png 371w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-8.1-a-63.2-300x136.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/p>\n<p>Question 64.<br \/>\n2x \u2212 3y + z = 4<br \/>\nx \u2212 2z = 1<br \/>\ny + z = 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/09\/eecfe5d0c1a2d55c4c19f5c2df4b2670\/8b1fa09e60c147c7d614ad4b0296a0e2\/lateximg.png?tcb=1621921169\" \/><\/p>\n<h3><a id=\"Lesson_8.2_Analyzing_Arithmetic_Sequences_and_Series\"><\/a>Lesson 8.2 Analyzing Arithmetic Sequences and Series<\/h3>\n<p><strong>Essential Question<\/strong> How can you recognize an arithmetic sequence from its graph?<br \/>\nIn an arithmetic sequence, the difference of consecutive terms, called the common difference, is constant. For example, in the arithmetic sequence 1, 4, 7, 10, . . . , the common difference is 3.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Recognizing Graphs of Arithmetic Sequences<br \/>\nWork with a partner. Determine whether each graph shows an arithmetic sequence. If it does, then write a rule for the nth term of the sequence, and use a spreadsheet to fond the sum of the first 20 terms. What do you notice about the graph of an arithmetic sequence?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38646\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 1\" width=\"442\" height=\"323\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-1.png 442w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-1-300x219.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Finding the Sum of an Arithmetic Sequence<br \/>\nWork with a partner. A teacher of German mathematician Carl Friedrich Gauss (1777\u20131855) asked him to find the sum of all the whole numbers from 1 through 100. To the astonishment of his teacher, Gauss came up with the answer after only a few moments. Here is what Gauss did:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38647\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 2\" width=\"478\" height=\"229\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-2.png 478w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-2-300x144.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\nExplain Gauss\u2019s thought process. Then write a formula for the sum Sn of the first n terms of an arithmetic sequence. Verify your formula by finding the sums of the first 20 terms of the arithmetic sequences in Exploration 1. Compare your answers to those you obtained using a spreadsheet.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you recognize an arithmetic sequence from its graph?<br \/>\nAnswer: Examine the graph is the shape of the graph is linear or not. If the graph is linear, then the shape of the graph is straight, then the given graph is an arithmetic sequence graph.<\/p>\n<p>Question 4.<br \/>\nFind the sum of the terms of each arithmetic sequence.<br \/>\na. 1, 4, 7, 10, . . . , 301<br \/>\nb. 1, 2, 3, 4, . . . , 1000<br \/>\nc. 2, 4, 6, 8, . . . , 800<br \/>\nAnswer:<br \/>\na. 1, 4, 7, 10, . . . , 301<br \/>\ntn = a + (n &#8211; 1)d<br \/>\n301 = 4 + (n &#8211; 1)3<br \/>\n301 = 4 + 3n &#8211; 3<br \/>\n301 = 3n + 1<br \/>\n3n = 300<br \/>\nn = 300\/3<br \/>\nn = 100<\/p>\n<p>b. 1, 2, 3, 4, . . . , 1000<br \/>\ntn = a + (n &#8211; 1)d<br \/>\n1000 = 2 + (n &#8211; 1)1<br \/>\n1000 = 2 + n &#8211; 1<br \/>\n1000 = n + 1<br \/>\nn = 999<\/p>\n<p>c. 2, 4, 6, 8, . . . , 800<br \/>\ntn = a + (n &#8211; 1)d<br \/>\n800 = 4 + (n &#8211; 1)2<br \/>\n800 = 4 + 2n &#8211; 2<br \/>\n800 = 2 + 2n<br \/>\n798 = 2n<br \/>\nn = 399<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Tell whether the sequence is arithmetic. Explain your reasoning.<\/strong><br \/>\nQuestion 1.<br \/>\n2, 5, 8, 11, 14, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112566\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-1.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-1.jpg\" width=\"211\" height=\"150\" \/><br \/>\nQuestion 2.<br \/>\n15, 9, 3, \u22123, \u22129, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112565\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-2.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-2.jpg\" width=\"192\" height=\"139\" \/><br \/>\nQuestion 3.<br \/>\n8, 4, 2, 1, \\(\\frac{1}{2}\\), . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112562\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-3.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-3.jpg\" width=\"141\" height=\"136\" \/><\/p>\n<p>Question 4.<br \/>\nWrite a rule for the nth term of the sequence 7, 11, 15, 19, . . .. Then find a<sub>15<\/sub>.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112564\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-4.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-4.jpg\" width=\"420\" height=\"229\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-4.jpg 420w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-4-300x164.jpg 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><\/p>\n<p><strong>Write a rule for the nth term of the sequence. Then graph the first six terms of the sequence.<\/strong><br \/>\nQuestion 5.<br \/>\na<sub>11<\/sub> = 50, d = 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112563\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-5.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-5.jpg\" width=\"384\" height=\"489\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-5.jpg 384w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-5-236x300.jpg 236w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/p>\n<p>Question 6.<br \/>\na<sub>7<\/sub> = 71, a<sub>16<\/sub> = 26<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112561\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-6.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-6.jpg\" width=\"421\" height=\"515\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-6.jpg 421w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-6-245x300.jpg 245w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><\/p>\n<p>Find the sum.<br \/>\nQuestion 7.<br \/>\n\\(\\sum_{i=1}^{10}\\)9i<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112560\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-7.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-7.jpg\" width=\"270\" height=\"196\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\sum_{k=1}^{12}\\)(7k + 2)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112559\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-8.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-9.jpg\" width=\"319\" height=\"217\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-8.jpg 319w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-8-300x204.jpg 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>Question 9.<br \/>\n\\(\\sum_{n=1}^{20}\\)(\u22124n + 6)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112557\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-9.jpg\" alt=\"\" width=\"328\" height=\"181\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-9.jpg 328w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-9-300x166.jpg 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Question 10.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 6, how many cards do you need to make a house of cards with eight rows?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112568\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-10.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-10.jpg\" width=\"413\" height=\"235\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-10.jpg 413w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.2-Answer-10-300x171.jpg 300w\" sizes=\"(max-width: 413px) 100vw, 413px\" \/><\/p>\n<h3><a id=\"Analyzing_Arithmetic_Sequences_and_Series_8.2_Exercises\"><\/a>Analyzing Arithmetic Sequences and Series 8.2 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe constant difference between consecutive terms of an arithmetic sequence is called the _______________.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45672\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 1\" width=\"535\" height=\"62\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-1.png 535w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-1-300x35.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38648\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 3\" width=\"421\" height=\"165\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-3.png 421w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-3-300x118.png 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/9675518776a3e85f794cd3d58f09b1f9\/e4083a86741d5e3b57fdb4b7ccd64abd\/lateximg.png?tcb=1621927725\" \/><\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, tell whether the sequence is arithmetic. Explain your reasoning.<\/strong><br \/>\nQuestion 3.<br \/>\n1, \u22121, \u22123, \u22125, \u22127, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/b171ac5dd33e1be214063db0b069e94b\/c699dad27421533b816a0c170030ac51\/lateximg.png?tcb=1621927746\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45673\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 3\" width=\"579\" height=\"59\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-3.png 579w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-3-300x31.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 4.<br \/>\n12, 6, 0, \u22126, \u221212, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/4616c8a088eb24b63b776651f2831d21\/83a1dd3c29143fc4020b8a965386e7c5\/lateximg.png?tcb=1621927760\" \/><\/p>\n<p>Question 5.<br \/>\n5, 8, 13, 20, 29, . . .<br \/>\nAnswer:<br \/>\na1 = 5<br \/>\na2 = 8<br \/>\n8 &#8211; 5 = 3<br \/>\n13 &#8211; 8 = 5<br \/>\nThe difference is not constant.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45674\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 5\" width=\"539\" height=\"60\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-5.png 539w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-5-300x33.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 6.<br \/>\n3, 5, 9, 15, 23, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/b47de41993d0acfaea566d0cd5e766fa\/4b7055e984077112c22a6761dd391321\/lateximg.png?tcb=1621927797\" \/><\/p>\n<p>Question 7.<br \/>\n36, 18, 9, \\(\\frac{9}{2}\\), \\(\\frac{9}{4}\\), . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45675\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 7\" width=\"530\" height=\"59\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-7.png 530w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-7-300x33.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 8.<br \/>\n81, 27, 9, 3, 1, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/b2ca8176fcf804c340199fc52dd07d70\/271d7ef3608d92ed3a3b21dd2aa6a655\/lateximg.png?tcb=1621927817\" \/><\/p>\n<p>Question 9.<br \/>\n\\(\\frac{1}{2}, \\frac{3}{4}, 1, \\frac{5}{4}, \\frac{3}{2}, \\ldots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45676\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 9\" width=\"590\" height=\"69\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-9.png 590w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-9-300x35.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\frac{1}{6}, \\frac{1}{2}, \\frac{5}{6}, \\frac{7}{6}, \\frac{3}{2}, \\ldots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/e4f92f9b02c9b81e99bd37a4357141c9\/41ba65ef87dd45f23788542c52a610ac\/lateximg.png?tcb=1621927836\" \/><\/p>\n<p>Question 11.<br \/>\n<strong>WRITING EQUATIONS<\/strong><br \/>\nWrite a rule for the arithmetic sequence with the given description.<br \/>\na. The first term is \u22123 and each term is 6 less than the previous term.<br \/>\nb. The first term is 7 and each term is 5 more than the previous term.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45677\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 11\" width=\"262\" height=\"345\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-11.png 262w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-11-228x300.png 228w\" sizes=\"(max-width: 262px) 100vw, 262px\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the terms of an arithmetic sequence when d &gt; 0 to when d &lt; 0.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/63dc93512237a01d4de81a3d82a969fb\/1167a94e067786c3af236183d0e03489\/lateximg.png?tcb=1621927861\" \/><\/p>\n<p><strong>In Exercises 13\u201320, write a rule for the nth term of the sequence. Then find a<sub>20<\/sub>.<\/strong><br \/>\nQuestion 13.<br \/>\n12, 20, 28, 36, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45678\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 13\" width=\"509\" height=\"229\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-13.png 509w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-13-300x135.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><\/p>\n<p>Question 14.<br \/>\n7, 12, 17, 22, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/21\/c0b111573a7702586cefb1fd32905528\/966910884912d0130dbcc21952498fa4\/lateximg.png?tcb=1621927876\" \/><\/p>\n<p>Question 15.<br \/>\n51, 48, 45, 42, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45679\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 15\" width=\"514\" height=\"229\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-15.png 514w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-15-300x134.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 16.<br \/>\n86, 79, 72, 65, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/f77952e246ccb14fdf27a36472445646\/a8d112774d78a3e67ca4b7a130e36587\/lateximg.png?tcb=1621927894\" \/><\/p>\n<p>Question 17.<br \/>\n\u22121, \u2212\\(\\frac{1}{3}\\), \\(\\frac{1}{3}\\), 1, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45680\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 17\" width=\"510\" height=\"242\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-17.png 510w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-17-300x142.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 18.<br \/>\n\u22122, \u2212\\(\\frac{5}{4}\\), \u2212\\(\\frac{1}{2}\\), \\(\\frac{1}{4}\\), . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/f72d5cb75439ae362834e190452a483b\/210caa083cfa6556fd4b6de34056f202\/lateximg.png?tcb=1621927911\" \/><\/p>\n<p>Question 19.<br \/>\n2.3, 1.5, 0.7, \u22120.1, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45681\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 19\" width=\"572\" height=\"227\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-19.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-19-300x119.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 20.<br \/>\n11.7, 10.8, 9.9, 9, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/a6b2df582f477b4f534943ff62ec3d87\/b34b940b1f3e5acc1b993a3d08b06a55\/lateximg.png?tcb=1621927929\" \/><\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 21 and 22, describe and correct the error in writing a rule for the nth term of the arithmetic sequence 22, 9, -4, -17, -30, . . ..<br \/>\nQuestion 21.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38649\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 4\" width=\"318\" height=\"106\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-4.png 318w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-4-300x100.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45682\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 21\" width=\"505\" height=\"129\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-21.png 505w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-21-300x77.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<p>Question 22.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38650\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 5\" width=\"321\" height=\"111\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-5.png 321w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-5-300x104.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/30\/22b2f790586df32a1636c5b2c60eb116\/5e6522c0c03922ec89af019b8936cf2b\/lateximg.png?tcb=1621927947\" \/><\/p>\n<p><strong>In Exercises 23\u201328, write a rule for the nth term of the sequence. Then graph the first six terms of the sequence.<\/strong><br \/>\nQuestion 23.<br \/>\na<sub>11<\/sub> = 43, d = 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45683\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 23\" width=\"506\" height=\"602\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-23.png 506w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-23-252x300.png 252w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p>Question 24.<br \/>\na<sub>13<\/sub> = 42, d = 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112575\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-24.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-24.jpg\" width=\"468\" height=\"650\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-24.jpg 468w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-24-216x300.jpg 216w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 25.<br \/>\na<sub>20<\/sub> = \u221227, d =\u22122<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45684\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 25\" width=\"505\" height=\"615\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-25.png 505w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-25-246x300.png 246w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<p>Question 26.<br \/>\na<sub>15<\/sub> = \u221235, d =\u22123<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112576\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-26.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-26.jpg\" width=\"422\" height=\"631\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-26.jpg 422w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-26-201x300.jpg 201w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Question 27.<br \/>\na<sub>17<\/sub> = \u22125, d = \u2212\\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45685\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 27\" width=\"507\" height=\"608\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-27.png 507w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-27-250x300.png 250w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 28.<br \/>\na<sub>21<\/sub> = \u221225, d = \u2212\\(\\frac{3}{2}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112577\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-28.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-28.jpg\" width=\"418\" height=\"684\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-28.jpg 418w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-28-183x300.jpg 183w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Question 29.<br \/>\n<strong>USING EQUATIONS<\/strong><br \/>\nOne term of an arithmetic sequence is a<sub>8<\/sub> = \u221213. The common difference is \u22128. What is a rule for the nth term of the sequence?<br \/>\nA. a<sub>n<\/sub> = 51 + 8n<br \/>\nB. a<sub>n<\/sub> = 35 + 8n<br \/>\nC. a<sub>n<\/sub> = 51 \u2212 8n<br \/>\nD. a<sub>n<\/sub> = 35 \u2212 8n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45686\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 29\" width=\"390\" height=\"307\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-29.png 390w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-29-300x236.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>FINDING A PATTERN<\/strong><br \/>\nOne term of an arithmetic sequence is a<sub>12<\/sub> = 43. The common difference is 6. What is another term of the sequence?<br \/>\nA. a<sub>3<\/sub> = \u221211<br \/>\nB. a<sub>4<\/sub> = \u221253<br \/>\nC. a<sub>5<\/sub> = 13<br \/>\nD. a<sub>6<\/sub> = \u221247<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112578\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-30.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-30.jpg\" width=\"359\" height=\"607\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-30.jpg 359w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-30-177x300.jpg 177w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p><strong>In Exercises 31\u201338, write a rule for the nth term of the arithmetic sequence.<\/strong><br \/>\nQuestion 31.<br \/>\na<sub>5<\/sub> = 41, a<sub>10<\/sub> = 96<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45687\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 31\" width=\"566\" height=\"413\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-31.png 566w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-31-300x219.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 32.<br \/>\na<sub>7<\/sub> = 58, a<sub>11<\/sub> = 94<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112579\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-32.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-32.jpg\" width=\"436\" height=\"826\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-32.jpg 436w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-32-158x300.jpg 158w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><\/p>\n<p>Question 33.<br \/>\na<sub>6<\/sub> =\u22128, a<sub>15<\/sub> = \u221262<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45688\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 33\" width=\"570\" height=\"410\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-33.png 570w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-33-300x216.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 34.<br \/>\na<sub>8<\/sub> = \u221215, a<sub>17<\/sub> = \u221278<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\na<sub>18<\/sub> = \u221259, a<sub>21<\/sub> = \u221271<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45689\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 35\" width=\"556\" height=\"415\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-35.png 556w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-35-300x224.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 36.<br \/>\na<sub>12<\/sub> = \u221238, a<sub>19<\/sub> = \u221273<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\na<sub>8<\/sub> = 12, a<sub>16<\/sub> = 22<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45690\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 37\" width=\"561\" height=\"438\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-37.png 561w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-37-300x234.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 38.<br \/>\na<sub>12<\/sub> = 9, a<sub>27<\/sub> = 15<br \/>\nAnswer:<\/p>\n<p><strong>WRITING EQUATIONS<\/strong> In Exercises 39\u201344, write a rule for the sequence with the given terms.<br \/>\nQuestion 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38651\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 6\" width=\"115\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45691\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 39\" width=\"577\" height=\"84\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-39.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-39-300x44.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38652\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 7\" width=\"116\" height=\"119\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/31\/9268df033b7a300f47b619d4620ebda4\/cc81059390410bf60f50ab86213ca82a\/lateximg.png?tcb=1621959349\" \/><\/p>\n<p>Question 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38653\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-8.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 8\" width=\"114\" height=\"159\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45692\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 41\" width=\"480\" height=\"90\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-41.png 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-41-300x56.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>Question 42.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38654\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 9\" width=\"107\" height=\"156\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/31\/1f9adcf71340b8a79a15a4df24970d6a\/69c6a89daf4c56f7b7a7a617f0816d70\/lateximg.png?tcb=1621959422\" \/><\/p>\n<p>Question 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38655\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-10.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 10\" width=\"248\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45693\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 43\" width=\"585\" height=\"93\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-43.png 585w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-43-300x48.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 44.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38656\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 11\" width=\"249\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/31\/29077e359df8bcfa0d4ecd10f07839c3\/e5c6ee4785aac833a7f72a6e7c2b9b9b\/lateximg.png?tcb=1621959485\" \/><\/p>\n<p>Question 45.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the graph of a<sub>n<\/sub> = 3n + 1, where n is a positive integer, with the graph of f(x) = 3x+ 1, where x is a real number.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45694\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 45\" width=\"557\" height=\"59\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-45.png 557w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-45-300x32.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nDescribe how doubling each term in an arithmetic sequence changes the common difference of the sequence. Justify your answer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/31\/d9bc370791208a6296311af84290d6d1\/e170eecf88d2eb3c8cffadf8a266ccc5\/lateximg.png?tcb=1621959548\" \/><\/p>\n<p><strong>In Exercises 47\u201352, find the sum.<\/strong><br \/>\nQuestion 47.<br \/>\n\\(\\sum_{i=1}^{20}\\)(2i \u2212 3)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45695\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 47\" width=\"334\" height=\"289\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-47.png 334w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-47-300x260.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Question 48.<br \/>\n\\(\\sum_{i=1}^{26}\\)(4i + 7)<br \/>\nAnswer:<br \/>\nFirst, we have to find the first and last terms.<br \/>\na1 = 4(1) + 7 = 11.<br \/>\na26 = 4(26) + 7 = 111.<br \/>\nS29 = 29(11 + 111\/2)<br \/>\n= 29(61)<br \/>\nS29 = 1,769<\/p>\n<p>Question 49.<br \/>\n\\(\\sum_{i=1}^{33}\\)(6 \u2212 2i )<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45696\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 49\" width=\"326\" height=\"291\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-49.png 326w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-49-300x268.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><\/p>\n<p>Question 50.<br \/>\n\\(\\sum_{i=1}^{31}\\)(\u22123 \u2212 4i )<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112709\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-50.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-50.jpg\" width=\"323\" height=\"236\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-50.jpg 323w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-50-300x219.jpg 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>Question 51.<br \/>\n\\(\\sum_{i=1}^{41}\\)(\u22122.3 + 0.1i )<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45697\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 51\" width=\"373\" height=\"290\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-51.png 373w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-51-300x233.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/p>\n<p>Question 52.<br \/>\n\\(\\sum_{i=1}^{39}\\)(\u22124.1 + 0.4i )<br \/>\nAnswer:<br \/>\nGiven,<br \/>\n\\(\\sum_{i=1}^{39}\\)(\u22124.1 + 0.4i )<br \/>\na1 = -4.1 + 0.4(1) = -3.7<br \/>\na39 = -4.1 + 0.4(39) = 11.5<br \/>\nS39 = 39(-3.7 + 11.5\/2)<br \/>\n= 39(3.9)<br \/>\nS39 = 152.1<\/p>\n<p><strong>NUMBER SENSE<\/strong> In Exercises 53 and 54, find the sum of the arithmetic sequence.<br \/>\nQuestion 53.<br \/>\nThe first 19 terms of the sequence 9, 2, \u22125, \u221212, . . ..<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45698\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 53\" width=\"567\" height=\"339\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-53.png 567w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-53-300x179.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 54.<br \/>\nThe first 22 terms of the sequence 17, 9, 1, \u22127, . . ..<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112713\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-54.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-54.jpg\" width=\"385\" height=\"412\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-54.jpg 385w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-54-280x300.jpg 280w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/p>\n<p>Question 55.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA marching band is arranged in rows. The first row has three band members, and each row after the first has two more band members than the row before it.<br \/>\na. Write a rule for the number of band members in the nth row.<br \/>\nb. How many band members are in a formation with seven rows?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38657\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-12.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 12\" width=\"222\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45699\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 55\" width=\"564\" height=\"449\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-55.png 564w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-55-300x239.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nDomestic bees make their honeycomb by starting with a single hexagonal cell, then forming ring after ring of hexagonal cells around the initial cell, as shown. The number of cells in successive rings forms an arithmetic sequence.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38658\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 13\" width=\"233\" height=\"92\" \/><br \/>\na. Write a rule for the number of cells in the nth ring.<br \/>\nb. How many cells are in the honeycomb after the ninth ring is formed?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112715\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-56.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-56.jpg\" width=\"586\" height=\"621\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-56.jpg 586w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-56-283x300.jpg 283w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 57.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nA quilt is made up of strips of cloth, starting with an inner square surrounded by rectangles to form successively larger squares. The inner square and all rectangles have a width of 1 foot. Write an expression using summation notation that gives the sum of the areas of all the strips of cloth used to make the quilt shown. Then evaluate the expression.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38659\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-14.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 14\" width=\"140\" height=\"128\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45700\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 57\" width=\"574\" height=\"347\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-57.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-57-300x181.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nWhich graph(s) represents an arithmetic sequence? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38660\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 15\" width=\"312\" height=\"284\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-15.png 312w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-15-300x273.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/26\/2ba00b040cbfa2878283d9e96aadd650\/3be03cdd2d3cccf1fa5a67be656ff270\/lateximg.png?tcb=1621961834\" width=\"561\" height=\"81\" \/><\/p>\n<p>Question 59.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend believes the sum of a series doubles when the common difference of an arithmetic series is doubled and the first term and number of terms in the series remain unchanged. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45701\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-59.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 59\" width=\"531\" height=\"160\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-59.png 531w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-59-300x90.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nIn number theory, the Dirichlet Prime Number Theorem states that if a and bare relatively prime, then the arithmetic sequence<br \/>\na, a + b, a + 2b, a + 3b, . . . contains infinitely many prime numbers. Find the first 10 primes in the sequence when a = 3 and b = 4.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112716\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-60.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-60.jpg\" width=\"456\" height=\"457\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-60.jpg 456w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-60-300x300.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Exercise-8.2-Answer-60-150x150.jpg 150w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><\/p>\n<p>Question 61.<br \/>\n<strong>REASONING<\/strong><br \/>\nFind the sum of the positive odd integers less than 300. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45702\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-61.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 61\" width=\"570\" height=\"415\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-61.png 570w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-61-300x218.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>USING EQUATIONS<\/strong><br \/>\nFind the value of n.<br \/>\na. \\(\\sum_{i=1}^{n}\\)(3i + 5) = 544<br \/>\nb. \\(\\sum_{i=1}^{n}\\)(\u22124i \u2212 1) = \u22121127<br \/>\nc. \\(\\sum_{i=5}^{n}\\)(7 + 12i) = 455<br \/>\nd. \\(\\sum_{i=3}^{n}\\)(\u22123 \u2212 4i) = \u2212507<br \/>\nAnswer:<br \/>\na. \\(\\sum_{i=1}^{n}\\)(3i + 5) = 544<br \/>\n3 \\(\\sum_{i=1}^{n}\\)(i + 5n) = 544<br \/>\n3n(n + 1)\/2 + 5n = 544<br \/>\n(3n\u00b2 + 13n)\/2 + 5n = 544<br \/>\n3n\u00b2 + 13n &#8211; 1088 = 0<br \/>\n(3n + 64) (n &#8211; 17) = 0<br \/>\nn = 17<br \/>\nn = -64\/3<br \/>\nn = -64\/3 is a negative value.<br \/>\nIt is not possible<br \/>\nn = 17<\/p>\n<p>b. \\(\\sum_{i=1}^{n}\\)(\u22124i \u2212 1) = \u22121127<br \/>\n-4(n)(n + 1)\/2 &#8211; n = -1127<br \/>\n2n(n + 1) + n = 1127<br \/>\n2n\u00b2 + 3n &#8211; 1127 = 0<br \/>\n(n &#8211; 23) (2n + 49) = 0<br \/>\nn = 23<br \/>\nn = -49\/2<br \/>\nn = -49\/2 is a negative value.<br \/>\nIt is not possible<br \/>\nn = 23<\/p>\n<p>c. \\(\\sum_{i=5}^{n}\\)(7 + 12i) = 455<br \/>\n(7 + 12(5)) + (7 + 12(6)) + &#8230;.(7 + 12n) = 455<br \/>\n7n &#8211; 28 + 6n\u00b2 + 6n &#8211; 120 = 455<br \/>\n6n\u00b2 + 13n &#8211; 603 = 0<br \/>\n(n &#8211; 9) (6n + 67) = 0<br \/>\nn = 9 or n = -67\/6<br \/>\nn = -67\/6 is a negative value.<br \/>\nn = 9<\/p>\n<p>d. \\(\\sum_{i=3}^{n}\\)(\u22123 \u2212 4i) = \u2212507<br \/>\n(-3 &#8211; 4(3)) + (-3 &#8211; 4(4)) + &#8230;. + (-3 &#8211; 4n) = -507<br \/>\n-3(n &#8211; 2) &#8211; 4(n &#8211; 2)(3 + n)\/2 = -507<br \/>\n-3(n &#8211; 2) &#8211; 2(n &#8211; 2) (n + 3) = 507<br \/>\n3n &#8211; 6 + 2n\u00b2 + 2n &#8211; 12 = 507<br \/>\n2n\u00b2 + 5n &#8211; 525 = 0<br \/>\n(n &#8211; 15)(2n + 35) = 0<br \/>\nn = 15 or n = -35\/2<br \/>\nn = -35\/2 is a negative value.<\/p>\n<p>Question 63.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nA theater has n rows of seats, and each row has d more seats than the row in front of it. There are x seats in the last (nth) row and a total of y seats in the entire theater. How many seats are in the front row of the theater? Write your answer in terms of n, x, and y.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45703\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-63.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 63\" width=\"564\" height=\"373\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-63.png 564w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-63-300x198.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe expressions 3 \u2212x, x, and 1 \u2212 3x are the first three terms in an arithmetic sequence. Find the value of x and the next term in the sequence.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe expressions 3 \u2212x, x, and 1 \u2212 3x are the first three terms in an arithmetic sequence.<br \/>\nx &#8211; (3 &#8211; x) = x &#8211; 3x &#8211; x<br \/>\nx &#8211; 3 + x = 1 &#8211; 4x<br \/>\n2x &#8211; 3 = 1 &#8211; 4x<br \/>\n2x + 4x = 1 + 3<br \/>\n6x = 4<br \/>\nx = 2\/3<br \/>\nThe next term is 3 &#8211; x, x, 1 &#8211; 3x<br \/>\na4 = a + 3d<br \/>\n3 &#8211; x + 3(2x &#8211; 3)<br \/>\n3 &#8211; x + 6x &#8211; 9<br \/>\n-6 + 5x<br \/>\n-6 + 5 \u00d7 (2\/3)<br \/>\n-6 + 10\/3<br \/>\n-18 + 10\/3<br \/>\na4 = -8\/3<br \/>\nThe value of x is 2\/3 and the next term in the sequence is -8\/3.<\/p>\n<p>Question 65.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nOne of the major sources of our knowledge of Egyptian mathematics is the Ahmes papyrus, which is a scroll copied in 1650 B.C. by an Egyptian scribe. The following problem is from the Ahmes papyrus.<br \/>\nDivide 10 hekats of barley among 10 men so that the common difference is \\(\\frac{1}{8}\\) of a hekat of barley.<br \/>\nUse what you know about arithmetic sequences and series to determine what portion of a hekat each man should receive.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45704\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-65.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 65\" width=\"539\" height=\"465\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-65.png 539w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-65-300x259.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 66.<br \/>\n\\(\\frac{7}{7^{1 \/ 3}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{7}{7^{1 \/ 3}}\\)<br \/>\n7\/7<sup>-3<\/sup><br \/>\n7\/7<sup>-3<\/sup>= 7 \u00d7 7<sup>3<\/sup><br \/>\n7 \u00d7 7 \u00d7 7 \u00d7 7 = 2401<br \/>\n\\(\\frac{7}{7^{1 \/ 3}}\\) = 2401<\/p>\n<p>Question 67.<br \/>\n\\(\\frac{3^{-2}}{3^{-4}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45705\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-67.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 67\" width=\"214\" height=\"45\" \/><\/p>\n<p>Question 68.<br \/>\n\\(\\left(\\frac{9}{49}\\right)^{1 \/ 2}\\)<br \/>\nAnswer:<br \/>\nGiven,<br \/>\n\\(\\left(\\frac{9}{49}\\right)^{1 \/ 2}\\)<br \/>\n\u221a9 = 3<br \/>\n\u221a49 = 7<br \/>\n\u221a(9\/49) = 3\/7<\/p>\n<p>Question 69.<br \/>\n(5<sup>1\/2<\/sup> \u2022 5<sup>1\/4<\/sup>)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45706\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-69.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 69\" width=\"280\" height=\"37\" \/><\/p>\n<p><strong>Tell whether the function represents exponential growth or exponential decay. Then graph the function.<\/strong><br \/>\nQuestion 70.<br \/>\ny= 2e<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\ny = e<sup>-3x<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45707\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-71.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 71\" width=\"397\" height=\"237\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-71.png 397w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-71-300x179.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><\/p>\n<p>Question 72.<br \/>\ny = 3e<sup>-x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\ny = e<sup>0.25x<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45708\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-73.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series 8.2 a 73\" width=\"417\" height=\"229\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-73.png 417w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-8.2-a-73-300x165.png 300w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><\/p>\n<h3><a id=\"Lesson_8.3_Analyzing_Geometric_Sequences_and_Series\"><\/a>Lesson 8.3 Analyzing Geometric Sequences and Series<\/h3>\n<p><strong>Essential Question<\/strong> How can you recognize a geometric sequence from its graph?<br \/>\nIn a geometric sequence, the ratio of any term to the previous term, called the common ratio, is constant. For example, in the geometric sequence 1, 2, 4, 8, . . . , the common ratio is 2.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Recognizing Graphs of Geometric Sequences<br \/>\nWork with a partner. Determine whether each graph shows a geometric sequence. If it does, then write a rule for the nth term of the sequence and use a spreadsheet to find the sum of the first 20 terms. What do you notice about the graph of a geometric sequence?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38661\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 1\" width=\"433\" height=\"332\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-1.png 433w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-1-300x230.png 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Finding the Sum of a Geometric Sequence<br \/>\nWork with a partner. You can write the nth term of a geometric sequence with the first term a1 and common ratio r as<br \/>\na<sub>n<\/sub> = a<sub>1<\/sub>r<sup>n-1<\/sup>.<br \/>\nSo, you can write the sum Sn of the first n terms of a geometric sequence as<br \/>\nS<sub>n<\/sub> = a<sub>1<\/sub> + a<sub>1<\/sub>r + a<sub>1<\/sub>r<sup>2<\/sup> + a<sub>1<\/sub>r<sup>3<\/sup> + . . . +a<sub>1<\/sub>r<sup>n-1<\/sup>.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38662\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 2\" width=\"221\" height=\"223\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-2.png 221w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-2-150x150.png 150w\" sizes=\"(max-width: 221px) 100vw, 221px\" \/><br \/>\nRewrite this formula by finding the difference S<sub>n<\/sub> \u2212 rS<sub>n<\/sub> and solve for S<sub>n<\/sub>. Then verify your rewritten formula by funding the sums of the first 20 terms of the geometric sequences exploration 1. Compare your answers to those you obtained using a spreadsheet.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you recognize a geometric sequence from its graph?<br \/>\nAnswer: Geometric sequences have a non-linear nature when graphed. The domain consists of the counting numbers 1, 2, 3, 4,&#8230; and the range consists of the actual terms of the sequence.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-186090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Lesson-8.3-Analyzing-Geometric-Sequences-and-Series_3-300x226.png\" alt=\"Big Ideas Math Answers Lesson 8.3 Analyzing Geometric Sequences and Series_3\" width=\"300\" height=\"226\" \/><\/p>\n<p>Question 4.<br \/>\nFind the sum of the terms of each geometric sequence.<br \/>\na. 1, 2, 4, 8, . . . , 8192<br \/>\nAnswer:<br \/>\na1 = 1<br \/>\nr = a2\/a1 = 2\/1 = 2<br \/>\ntn = 8192<br \/>\n8192 = 1 \u00d7 2<sup>n-1<\/sup><br \/>\n2<sup>13<\/sup> = 2<sup>n-1<\/sup><br \/>\nwhen n = 14<br \/>\nSn = a(r<sup>n<\/sup> &#8211; 1) \u00d7 1\/r &#8211; 1<br \/>\nSn = 1(16384 &#8211; 1) \u00d7 1\/2-1<br \/>\nSn = 16383<\/p>\n<p>b. 0.1, 0.01, 0.001, 0.0001, . . . , 10<sup>-10<\/sup><br \/>\nAnswer:<br \/>\n0.1, 0.01, 0.001, 0.0001, . . . , 10<sup>-10<\/sup><br \/>\nan = 10^-10<br \/>\nr = 0.01\/0.1 = 1\/10<br \/>\n10<sup>-10 <\/sup>= 1 . (1\/10)<sup>n-1<\/sup><br \/>\n(1\/10)<sup>10<\/sup> = 1\/10<sup>n-1<\/sup><br \/>\n10 = n &#8211; 1<br \/>\nn &#8211; 1 = 10<br \/>\nn = 11<br \/>\nSn = a1\/1 &#8211; r<br \/>\nSn = 0.1\/0.9<br \/>\nSn = 1\/9<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Tell whether the sequence is geometric. Explain your reasoning.<\/strong><br \/>\nQuestion 1.<br \/>\n27, 9, 3, 1, \\(\\frac{1}{3}\\), . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112873\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-1.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-1.jpg\" width=\"436\" height=\"244\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-1.jpg 436w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-1-300x168.jpg 300w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><\/p>\n<p>Question 2.<br \/>\n2, 6, 24, 120, 720, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112874\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-2.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-1.jpg\" width=\"427\" height=\"193\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-2.jpg 427w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-2-300x136.jpg 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<p>Question 3.<br \/>\n\u22121, 2, \u22124, 8, \u221216, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112875\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-3.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-1.jpg\" width=\"405\" height=\"195\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-3.jpg 405w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-3-300x144.jpg 300w\" sizes=\"(max-width: 405px) 100vw, 405px\" \/><\/p>\n<p>Question 4.<br \/>\nWrite a rule for the nth term of the sequence 3, 15, 75, 375, . . .. Then find a<sub>9<\/sub>.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112876\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-4.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-4.jpg\" width=\"406\" height=\"182\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-4.jpg 406w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-4-300x134.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p><strong>Write a rule for the nth term of the sequence. Then graph the first six terms of the sequence.<\/strong><br \/>\nQuestion 5.<br \/>\na<sub>6<\/sub> = \u221296, r = \u22122<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112877\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-5.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-5.jpg\" width=\"429\" height=\"758\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-5.jpg 429w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-5-170x300.jpg 170w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><\/p>\n<p>Question 6.<br \/>\na<sub>2<\/sub> = 12, a<sub>4<\/sub> = 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112878\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-6.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-6.jpg\" width=\"532\" height=\"887\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-6.jpg 532w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-6-180x300.jpg 180w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p><strong>Find the sum.<\/strong><br \/>\nQuestion 7.<br \/>\n\\(\\sum_{k=1}^{8}\\)5<sup>k\u22121<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112883\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-7JPG.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-7JPG.jpg\" width=\"396\" height=\"209\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-7JPG.jpg 396w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-7JPG-300x158.jpg 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\sum_{i=1}^{12}\\)6(\u22122)<sup>i\u22121<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-8.jpg\" \/><\/p>\n<p>Question 9.<br \/>\n\\(\\sum_{i=1}^{7}\\)\u221216(0.5)<sup>t\u22121<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112880\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-9.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-9.jpg\" width=\"379\" height=\"205\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-9.jpg 379w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-9-300x162.jpg 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/p>\n<p>Question 10.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 6, how does the monthly payment change when the annual interest rate is 5%?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112881\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-10.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-10.jpg\" width=\"388\" height=\"459\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-10.jpg 388w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-monitoring-progress-8.3-Answer-10-254x300.jpg 254w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<h3><a id=\"Analyzing_Geometric_Sequences_and_Series_8.3_Exercises\"><\/a>Analyzing Geometric Sequences and Series 8.3 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe constant ratio of consecutive terms in a geometric sequence is called the __________.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45709\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 1\" width=\"513\" height=\"64\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-1.png 513w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-1-300x37.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow can you determine whether a sequence is geometric from its graph?<br \/>\nAnswer:<br \/>\nThe Graphing of a geometric sequence behaves like a graph of an exponential function. By observing the graph we can determine whether the sequence is geometric or not.<\/p>\n<p>Question 3.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe nth term of a geometric sequence has the form a<sub>n<\/sub> = ___________.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45710\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 3\" width=\"478\" height=\"66\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-3.png 478w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-3-300x41.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nState the rule for the sum of the first n terms of a geometric series.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/03\/31\/c3f566c8f1d80571449e11707c8a3c25\/62aecb834621d893150c7cb7b5f4aa59\/lateximg.png?tcb=1622013098\" \/><\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201312, tell whether the sequence is geometric. Explain your reasoning.<\/strong><br \/>\nQuestion 5.<br \/>\n96, 48, 24, 12, 6, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45711\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 5\" width=\"531\" height=\"119\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-5.png 531w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-5-300x67.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 6.<br \/>\n729, 243, 81, 27, 9, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/6a7f135cccaa4ebfbaf5bbcd5f3f0e5f\/f458254d334962af97a61bdd124f22f7\/lateximg.png?tcb=1622013115\" \/><\/p>\n<p>Question 7.<br \/>\n2, 4, 6, 8, 10, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45712\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-7.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 7\" width=\"578\" height=\"83\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-7.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-7-300x43.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 8.<br \/>\n5, 20, 35, 50, 65, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/826fe79af6122a9bb98c3cbb0b3360d6\/5ecf0b7e8815952463d9617ca70625ce\/lateximg.png?tcb=1622013136\" \/><\/p>\n<p>Question 9.<br \/>\n0.2, 3.2, \u221212.8, 51.2, \u2212204.8, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45713\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-9.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 9\" width=\"559\" height=\"90\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-9.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-9-300x48.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 10.<br \/>\n0.3, \u22121.5, 7.5, \u221237.5, 187.5, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/69e26f044564e8a3eb7a6bde390e9f41\/40e7afb790a1dcb7b4796702974d40e6\/lateximg.png?tcb=1622013158\" \/><\/p>\n<p>Question 11.<br \/>\n\\(\\frac{1}{2}, \\frac{1}{6}, \\frac{1}{18}, \\frac{1}{54}, \\frac{1}{162}, \\ldots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45714\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-11.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 11\" width=\"424\" height=\"289\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-11.png 424w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-11-300x204.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>Question 12.<br \/>\n\\(\\frac{1}{4}, \\frac{1}{16}, \\frac{1}{64}, \\frac{1}{256}, \\frac{1}{1024}, \\ldots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/b57a7d5a5cdaa734f31b7f68a237d35c\/0d8f0bc60a198d24df2a8b3b096c348f\/lateximg.png?tcb=1622013179\" \/><\/p>\n<p>Question 13.<br \/>\n<strong>WRITING EQUATIONS<\/strong><br \/>\nWrite a rule for the geometric sequence with the given description.<br \/>\na. The first term is \u22123, and each term is 5 times the previous term.<br \/>\nb. The first term is 72, and each term is \\(\\frac{1}{3}\\) times the previous term.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45715\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-13.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 13\" width=\"588\" height=\"143\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-13.png 588w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-13-300x73.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 14.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the terms of a geometric sequence when r &gt; 1 to when 0 &lt; r &lt; 1.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/6488c0b52efe3ccdf5e839aeb01e6c75\/27fe0ad63d565839479ef38de720763b\/lateximg.png?tcb=1622013197\" \/><\/p>\n<p><strong>In Exercises 15\u201322, write a rule for the nth term of the sequence. Then find a<sub>7<\/sub>.<\/strong><br \/>\nQuestion 15.<br \/>\n4, 20, 100, 500, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45716\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-15.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 15\" width=\"460\" height=\"175\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-15.png 460w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-15-300x114.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/p>\n<p>Question 16.<br \/>\n6, 24, 96, 384, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/deffb23c69d4fd89fa5e135bb1186afd\/454b3abf4e38db9e44568cbbf0d9bc58\/lateximg.png?tcb=1622013213\" \/><\/p>\n<p>Question 17.<br \/>\n112, 56, 28, 14, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45717\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-17.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 17\" width=\"486\" height=\"205\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-17.png 486w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-17-300x127.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 18.<br \/>\n375, 75, 15, 3, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/b05cd53b2c4ab6ac4e761af3889a98dc\/97185e1eb044860abf1965bc9a096461\/lateximg.png?tcb=1622013226\" \/><\/p>\n<p>Question 19.<br \/>\n4, 6, 9, \\(\\frac{27}{2}\\), . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45718\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-19.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 19\" width=\"463\" height=\"196\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-19.png 463w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-19-300x127.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/p>\n<p>Question 20.<br \/>\n2, \\(\\frac{3}{2}\\), \\(\\frac{9}{8}\\), \\(\\frac{27}{32}\\), . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/4ab51ea3684e221cb5be974f98fee20c\/cbf05631076dabce626407a79472abf5\/lateximg.png?tcb=1622013243\" \/><\/p>\n<p>Question 21.<br \/>\n1.3, \u22123.9, 11.7, \u221235.1, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45719\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-21.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 21\" width=\"497\" height=\"174\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-21.png 497w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-21-300x105.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/p>\n<p>Question 22.<br \/>\n1.5, \u22127.5, 37.5, \u2212187.5, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/73c3854014230f3c48ca8b9503b74101\/1a6130ca3132c7b641dfc74641c4b325\/lateximg.png?tcb=1622013262\" \/><\/p>\n<p><strong>In Exercises 23\u201330, write a rule for the nth term of the sequence. Then graph the first six terms of the sequence.<\/strong><br \/>\nQuestion 23.<br \/>\na<sub>3<\/sub> = 4, r = 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45720\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-23.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 23\" width=\"511\" height=\"548\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-23.png 511w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-23-280x300.png 280w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>Question 24.<br \/>\na<sub>3<\/sub> = 27, r = 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112893\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-24.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-24.jpg\" width=\"474\" height=\"674\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-24.jpg 474w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-24-211x300.jpg 211w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>Question 25.<br \/>\na<sub>2<\/sub> = 30, r = \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45721\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-25.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 25\" width=\"539\" height=\"547\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-25.png 539w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-25-296x300.png 296w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 26.<br \/>\na<sub>2<\/sub> = 64, r = \\(\\frac{1}{4}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112897\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-26.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-26.jpg\" width=\"473\" height=\"653\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-26.jpg 473w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-26-217x300.jpg 217w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<p>Question 27.<br \/>\na<sub>4<\/sub> = \u2212192, r = 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45722\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-27.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 27\" width=\"559\" height=\"498\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-27.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-27-300x267.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 28.<br \/>\na<sub>4<\/sub> = \u2212500, r = 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112898\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-28.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-28.jpg\" width=\"502\" height=\"699\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-28.jpg 502w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-28-215x300.jpg 215w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Question 29.<br \/>\na<sub>5<\/sub> = 3, r =\u2212 \\(\\frac{1}{3}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45723\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-29.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 29\" width=\"546\" height=\"550\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-29.png 546w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-29-298x300.png 298w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-29-150x150.png 150w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 30.<br \/>\na<sub>5<\/sub> = 1, r = \u2212\\(\\frac{1}{5}\\)<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 31 and 32, describe and correct the error in writing a rule for the nth term of the geometric sequence for which a<sub>2<\/sub> = 48 and r = 6.<br \/>\nQuestion 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38663\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 3\" width=\"233\" height=\"116\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45724\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-31.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 31\" width=\"346\" height=\"204\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-31.png 346w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-31-300x177.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38664\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-4.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 4\" width=\"242\" height=\"116\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/6966879d53dd9b707df688db21703b20\/1fa6bc23f6dadeb27095d494c2ba6bff\/lateximg.png?tcb=1622013732\" \/><\/p>\n<p><strong>In Exercises 33\u201340, write a rule for the nth term of the geometric sequence.<\/strong><br \/>\nQuestion 33.<br \/>\na<sub>2<\/sub> = 28, a<sub>5<\/sub> = 1792<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45725\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-33.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 33\" width=\"570\" height=\"427\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-33.png 570w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-33-300x225.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 34.<br \/>\na<sub>1<\/sub> = 11, a<sub>4<\/sub> = 88<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/736ebb6f977250f55e9d2bbb12f4f796\/338018ce22338cd1816ab8bc4d7e15ec\/lateximg.png?tcb=1622013752\" \/><\/p>\n<p>Question 35.<br \/>\na<sub>1<\/sub> =\u22126, a<sub>5<\/sub> = \u2212486<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45726\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-35.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 35\" width=\"503\" height=\"240\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-35.png 503w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-35-300x143.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p>Question 36.<br \/>\na<sub>2<\/sub> = \u221210, a<sub>6<\/sub> =\u22126250<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/01\/8b008e78775c9d5daa7d2ccd9f5bfb1a\/99c3a55f8b11e23e9459b27b1c0eeda1\/lateximg.png?tcb=1622013768\" \/><\/p>\n<p>Question 37.<br \/>\na<sub>2<\/sub> = 64, a<sub>4<\/sub> = 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45727\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-37.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 37\" width=\"558\" height=\"537\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-37.png 558w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-37-300x289.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 38.<br \/>\na<sub>1<\/sub> = 1, a<sub>2<\/sub> = 49<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/02\/af9d08b1b9b7eb79ebad684929e79e6f\/e982db508104c5e59d431eb57dd96930\/lateximg.png?tcb=1622013787\" \/><\/p>\n<p>Question 39.<br \/>\na<sub>2<\/sub> =\u221272, a<sub>6<\/sub> = \u2212\\(\\frac{1}{18}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45728\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-39.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 39\" width=\"551\" height=\"546\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-39.png 551w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-39-300x297.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-39-150x150.png 150w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 40.<br \/>\na<sub>2<\/sub> =\u221248, a<sub>5<\/sub> = \\(\\frac{3}{4}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/70f29f575a4ef8e8de3c3d8cf0a369ff\/dbfda9ac69e26a4b4aef0f0904344656\/lateximg.png?tcb=1622013803\" \/><\/p>\n<p><strong>WRITING EQUATIONS<\/strong> In Exercises 41\u201346, write a rule for the sequence with the given terms.<br \/>\nQuestion 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38665\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 5\" width=\"116\" height=\"160\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45729\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-41.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 41\" width=\"526\" height=\"99\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-41.png 526w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-41-300x56.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 42.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38666\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-6.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 6\" width=\"118\" height=\"158\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/f578397e895184a63f57a4be8b482e2a\/39bd58606e3e7f8028e44aa0808a2480\/lateximg.png?tcb=1622013821\" \/><\/p>\n<p>Question 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38667\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-7.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 7\" width=\"129\" height=\"160\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45730\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-43.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 43\" width=\"510\" height=\"131\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-43.png 510w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-43-300x77.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 44.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38668\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-8.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 8\" width=\"115\" height=\"156\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/0d99cce69b591300805349df641a984d\/10921da5ef24f7f053fc9894efaf25ef\/lateximg.png?tcb=1622013840\" \/><\/p>\n<p>Question 45.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38669\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-9.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 9\" width=\"308\" height=\"68\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-9.png 308w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-9-300x66.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45731\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-45.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 45\" width=\"538\" height=\"107\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-45.png 538w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-45-300x60.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 46.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38670\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-10.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 10\" width=\"304\" height=\"70\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-10.png 304w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-10-300x69.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/457df8b6199e7750041fefb09c6318a2\/c1c6c447bc93a940de47df9aef7a1bd6\/lateximg.png?tcb=1622013856\" \/><\/p>\n<p><strong>In Exercises 47\u201352, find the sum.<\/strong><br \/>\nQuestion 47.<br \/>\n\\(\\sum_{i=1}^{9}\\)6(7)<sup>i\u22121<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45732\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-47.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 47\" width=\"468\" height=\"294\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-47.png 468w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-47-300x188.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 48.<br \/>\n\\(\\sum_{i=1}^{10}\\)7(4)<sup>i\u22121<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/f4603bb8adcd99aa1129ec2faad8dee7\/a07b02373a4fc119eed499b9cde75216\/lateximg.png?tcb=1622013876\" \/><\/p>\n<p>Question 49.<br \/>\n\\(\\sum_{i=1}^{10}\\)4(\\(\\frac{3}{4}\\))<sup>i\u22121<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45733\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-49.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 49\" width=\"465\" height=\"426\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-49.png 465w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-49-300x275.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><\/p>\n<p>Question 50.<br \/>\n\\(\\sum_{i=1}^{8}\\)5(\\(\\frac{1}{3}\\))<sup>i\u22121<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/b61e6c0df38339b0622efe15286323c8\/647ee98a75ff5e609612fb70c8b72dfa\/lateximg.png?tcb=1622013893\" \/><\/p>\n<p>Question 51.<br \/>\n\\(\\sum_{i=0}^{8}\\)8(\u2212\\(\\frac{2}{3}\\))<sup>i<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45734\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-51.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 51\" width=\"528\" height=\"754\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-51.png 528w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-51-210x300.png 210w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 52.<br \/>\n\\(\\sum_{i=0}^{0}\\)9(\u2212\\(\\frac{3}{4}\\))<sup>i<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/e3f6d6424dd08cd1d9f17358bcd15b98\/e301743c05072b56a046513b84cfeae9\/lateximg.png?tcb=1622013910\" \/><\/p>\n<p><strong>NUMBER SENSE<\/strong> In Exercises 53 and 54, find the sum.<br \/>\nQuestion 53.<br \/>\nThe first 8 terms of the geometric sequence \u221212, \u221248, \u2212192, \u2212768, . . ..<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45735\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-53.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 53\" width=\"333\" height=\"286\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-53.png 333w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-53-300x258.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p>Question 54.<br \/>\nThe first 9 terms of the geometric sequence \u221214, \u221242, \u2212126, \u2212378, . . ..<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/11f7f3cb1e41497b9b4596755ddbf890\/c46194816ff593d4a5d83a9ad57f803a\/lateximg.png?tcb=1622013930\" \/><\/p>\n<p>Question 55.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the graph of a<sub>n<\/sub> = 5(3)<sup>n\u22121<\/sup>, where n is a positive integer, to the graph of f(x) = 5 \u2022 3<sup>x\u22121<\/sup>, where x is a real number.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45736\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-55.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 55\" width=\"590\" height=\"58\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-55.png 590w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-55-300x29.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nUse the rule for the sum of a finite geometric series to write each polynomial as a rational expression.<br \/>\na. 1 + x + x<sup>2<\/sup> + x<sup>3<\/sup> + x<sup>4<\/sup><br \/>\nb. 3x + 6x<sup>3<\/sup> + 12x<sup>5<\/sup> + 24x<sup>7<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112899\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-56.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-56.jpg\" width=\"430\" height=\"521\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-56.jpg 430w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-56-248x300.jpg 248w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><\/p>\n<p><strong>MODELING WITH MATHEMATICS<\/strong> In Exercises 57 and 58, use the monthly payment formula given in Example 6.<br \/>\nQuestion 57.<br \/>\nYou are buying a new car. You take out a 5-year loan for $15,000. The annual interest rate of the loan is 4%. Calculate the monthly payment.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45737\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-57.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 57\" width=\"569\" height=\"354\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-57.png 569w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-57-300x187.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 58.<br \/>\nYou are buying a new house. You take out a 30-year mortgage for $200,000. The annual interest rate of the loan is 4.5%. Calculate the monthly payment.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38671\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-11.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 11\" width=\"157\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/27\/09df850087e7004a1839f0dca7d351e4\/9d019fef4215ef2fa6aa1e92f58f1d8c\/lateximg.png?tcb=1622014105\" \/><\/p>\n<p>Question 59.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA regional soccer tournament has 64 participating teams. In the first round of the tournament, 32 games are played. In each successive round, the number of games decreases by a factor of \\(\\frac{1}{2}\\).<br \/>\na. Write a rule for the number of games played in the nth round. For what values of n does the rule make sense? Explain.<br \/>\nb. Find the total number of games played in the regional soccer tournament.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45738\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-59.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 59\" width=\"554\" height=\"418\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-59.png 554w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-59-300x226.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn a skydiving formation with R rings, each ring after the first has twice as many skydivers as the preceding ring. The formation for R = 2 is shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38672\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-12.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 12\" width=\"193\" height=\"147\" \/><br \/>\na. Let an be the number of skydivers in the nth ring. Write a rule for a<sub>n<\/sub>.<br \/>\nb. Find the total number of skydivers when there are four rings.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112901\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-60.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-60.jpg\" width=\"544\" height=\"558\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-60.jpg 544w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-60-292x300.jpg 292w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 61.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe Sierpinski carpet is a fractal created using squares. The process involves removing smaller squares from larger squares. First, divide a large square into nine congruent squares. Then remove the center square. Repeat these steps for each smaller square, as shown below. Assume that each side of the initial square is 1 unit long.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38673\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-13.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 13\" width=\"325\" height=\"120\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-13.png 325w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-13-300x111.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\na. Let a<sub>n<\/sub> be the total number of squares removed at the nth stage. Write a rule for an. Then find the total number of squares removed through Stage 8.<br \/>\nb. Let b<sub>n<\/sub> be the remaining area of the original square after the nth stage. Write a rule for b<sub>n<\/sub>. Then find the remaining area of the original square after Stage 12.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45739\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-61.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 61\" width=\"565\" height=\"438\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-61.png 565w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-61-300x233.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nMatch each sequence with its graph. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38674\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-14.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 14\" width=\"322\" height=\"205\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-14.png 322w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-14-300x191.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112902\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-62.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-62.jpg\" width=\"410\" height=\"326\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-62.jpg 410w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-62-300x239.jpg 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><\/p>\n<p>Question 63.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nOn January 1, you deposit $2000 in a retirement account that pays 5% annual interest. You make this deposit each January 1 for the next 30 years. How much money do you have in your account immediately after you make your last deposit?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45740\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-63.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 63\" width=\"390\" height=\"89\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-63.png 390w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-63-300x68.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe first four iterations of the fractal called the Koch snowflake are shown below. Find the perimeter and area of each iteration. Do the perimeters and areas form geometric sequences? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38675\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-15.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 15\" width=\"327\" height=\"101\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-15.png 327w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-15-300x93.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112903\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-64.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-64.jpg\" width=\"437\" height=\"691\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-64.jpg 437w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-64-190x300.jpg 190w\" sizes=\"(max-width: 437px) 100vw, 437px\" \/><\/p>\n<p>Question 65.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYou and your friend are comparing two loan options for a $165,000 house. Loan 1 is a 15-year loan with an annual interest rate of 3%. Loan 2 is a 30-year loan with an annual interest rate of 4%. Your friend claims the total amount repaid over the loan will be less for Loan 2. Is your friend correct? Justify your answer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45741\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-65.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 65\" width=\"500\" height=\"475\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-65.png 500w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-65-300x285.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p>Question 66.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nLet L be the amount of a loan (in dollars), i be the monthly interest rate (in decimal form), t be the term (in months), and M be the monthly payment (in dollars).<br \/>\na. When making monthly payments, you are paying the loan amount plus the interest the loan gathers each month. For a 1-month loan, t= 1, the equation for repayment is L(1 +i) \u2212M= 0. For a 2-month loan, t= 2, the equation is [L(1 + i) \u2212M](1 + i) \u2212M = 0. Solve both of these repayment equations for L.<br \/>\nb. Use the pattern in the equations you solved in part (a) to write a repayment equation for a t-month loan. (Hint: L is equal to M times a geometric series.) Then solve the equation for M.<br \/>\nc. Use the rule for the sum of a finite geometric series to show that the formula in part (b) is equivalent to<br \/>\nM = L\\(\\left(\\frac{i}{1-(1+i)^{-t}}\\right)\\).<br \/>\nUse this formula to check your answers in Exercises 57 and 58.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112905\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-66.jpg\" alt=\"\" width=\"508\" height=\"787\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-66.jpg 508w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-66-194x300.jpg 194w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Graph the function. State the domain and range.<\/strong><br \/>\nQuestion 67.<br \/>\nf(x) = \\(\\frac{1}{x-3}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45742\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-67.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 67\" width=\"398\" height=\"360\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-67.png 398w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-67-300x271.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p>\n<p>Question 68.<br \/>\ng(x) = \\(\\frac{2}{x}\\) + 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112907\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-68.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-68.jpg\" width=\"562\" height=\"810\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-68.jpg 562w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-68-208x300.jpg 208w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 69.<br \/>\nh(x) = \\(\\frac{1}{x-2}\\) + 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45743\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-69.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 a 69\" width=\"383\" height=\"359\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-69.png 383w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-a-69-300x281.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n<p>Question 70.<br \/>\np(x) = \\(\\frac{3}{x+1}\\) \u2212 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112908\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-70.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-70.jpg\" width=\"627\" height=\"834\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-70.jpg 627w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.3-Answer-70-226x300.jpg 226w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/><\/p>\n<h3><a id=\"Sequences_and_Series_Study_Skills:_Keeping_Your_Mind_Focused\"><\/a>Sequences and Series Study Skills: Keeping Your Mind Focused<\/h3>\n<p><strong>8.1\u20138.3 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38676\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-16.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 16\" width=\"655\" height=\"91\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-16.png 655w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-16-300x42.png 300w\" sizes=\"(max-width: 655px) 100vw, 655px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 8.1Sequences, p. 410<br \/>\nSeries and Summation Notation, p. 412<br \/>\nFormulas for Special Series, p. 413<\/p>\n<p>Section 8.2<br \/>\nRule for an Arithmetic Sequence, p. 418<br \/>\nThe Sum of a Finite Arithmetic Series, p. 420<\/p>\n<p>Section 8.3<br \/>\nRule for a Geometric Sequence, p. 426<br \/>\nThe Sum of a Finite Geometric Series, p. 428<\/p>\n<p><strong>Mathematical Practices<\/strong><br \/>\nQuestion 1.<br \/>\nExplain how viewing each arrangement as individual tables can be helpful in Exercise 29 on page 415.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nHow can you use tools to find the sum of the arithmetic series in Exercises 53 and 54 on page 423?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nHow did understanding the domain of each function help you to compare the graphs in Exercise 55 on page 431?<br \/>\nAnswer:<\/p>\n<p><strong>Study Skills: Keeping Your Mind Focused<\/strong><\/p>\n<p>\u2022 Before doing homework, review the concept boxes and examples. Talk through the examples out loud.<br \/>\n\u2022 Complete homework as though you were also preparing for a quiz. Memorize the different types of problems, formulas, rules, and so on.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38677\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-17.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series 8.3 17\" width=\"362\" height=\"267\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-17.png 362w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-8.3-17-300x221.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><\/p>\n<h3><a id=\"Sequences_and_Series_8.1_\u2013_8.3_Quiz\"><\/a>Sequences and Series 8.1 \u2013 8.3 Quiz<\/h3>\n<p>Describe the pattern, write the next term, and write a rule for the nth term of the sequence.<br \/>\nQuestion 1.<br \/>\n1, 7, 13, 19, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/2ae7090f9fe7c704008aafd3a79f77fe\/f18420ff86af3fbdd867cb7432a6bb34\/lateximg.png?tcb=1622021946\" \/><\/p>\n<p>Question 2.<br \/>\n\u22125, 10, \u221215, 20, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/7412cda982dd4bb438017d34e4d5612c\/270c6b0b8bf701b8dd40b2cf49b1ddc9\/lateximg.png?tcb=1622022029\" \/><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{20}, \\frac{2}{30}, \\frac{3}{40}, \\frac{4}{50}, \\ldots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/87b87604ea10783ede06c95855ffc28e\/bab409acf795e53550c7063f5a8236bd\/lateximg.png?tcb=1622022051\" \/><\/p>\n<p><strong>Write the series using summation notation. Then find the sum of the series.<\/strong><br \/>\nQuestion 4.<br \/>\n1 + 2 + 3 + 4 +. . .+ 15<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/d2a8ebcda4e57a2ca48d105a9a006867\/6c18415793dcc233fa9f45a01a9a44b0\/lateximg.png?tcb=1622022079\" \/><\/p>\n<p>Question 5.<br \/>\n\\(0+\\frac{1}{2}+\\frac{2}{3}+\\frac{3}{4}+\\cdots+\\frac{7}{8}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/46a256037d4a16c9cc3533e058ab5e8e\/92ec2727c0aef141cf94ffa3124fbd0b\/lateximg.png?tcb=1622022094\" \/><\/p>\n<p>Question 6.<br \/>\n9 + 16 + 25 + . . .+ 100<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/aeca5086e4202077f7c5cca924488e91\/d9ba3e84bc4b206cfee183630ea8aabc\/lateximg.png?tcb=1622022109\" \/><\/p>\n<p><strong>Write a rule for the nth term of the sequence.<\/strong><br \/>\nQuestion 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38678\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-q-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series q 1\" width=\"138\" height=\"163\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/f7185e10701ba97d3d35fcf1a215ccd7\/559b8522868b879457f3667d11c07fbb\/lateximg.png?tcb=1622022125\" \/><\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38679\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-q-2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series q 2\" width=\"141\" height=\"165\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/05\/7ffc08c2fe09c16ab011257a6574a343\/2e7a4d50a15f591685199d4e7c87c454\/lateximg.png?tcb=1622022139\" \/><\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38680\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-q-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series q 3\" width=\"129\" height=\"164\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/06\/363798d421b7c95a84fe4e81c27061bf\/2bf632f33a4af514e068962c8dfb50f6\/lateximg.png?tcb=1622022155\" \/><\/p>\n<p><strong>Tell whether the sequence is arithmetic, geometric, or neither. Write a rule for the nth term of the sequence. Then find a<sub>9<\/sub>.<\/strong><br \/>\nQuestion 10.<br \/>\n13, 6, \u22121, \u22128, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/06\/add1733646d5608f21e35325241b1c68\/70daa2ddee6a4c04c64d3f613b99c74e\/lateximg.png?tcb=1622022177\" \/><\/p>\n<p>Question 11.<br \/>\n\\(\\frac{1}{2}, \\frac{1}{3}, \\frac{1}{4}, \\frac{1}{5}, \\ldots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112938\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.11JPG.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.11JPG.jpg\" width=\"563\" height=\"579\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.11JPG.jpg 563w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.11JPG-292x300.jpg 292w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 12.<br \/>\n1, \u22123, 9, \u221227, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112942\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.12JPG.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.12JPG.jpg\" width=\"547\" height=\"588\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.12JPG.jpg 547w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.12JPG-279x300.jpg 279w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 13.<br \/>\nOne term of an arithmetic sequence is a<sub>12<\/sub> = 19. The common difference is d = 7. Write a rule for the nth term. Then graph the first six terms of the sequence.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112944\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.13JPG.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.13JPG.jpg\" width=\"494\" height=\"665\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.13JPG.jpg 494w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.13JPG-223x300.jpg 223w\" sizes=\"(max-width: 494px) 100vw, 494px\" \/><\/p>\n<p>Question 14.<br \/>\nTwo terms of a geometric sequence are a<sub>6<\/sub> = \u221250 and a<sub>9<\/sub> = \u22126250. Write a rule for the nth term.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112946\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.14JPG.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.14JPG.jpg\" width=\"535\" height=\"731\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.14JPG.jpg 535w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.14JPG-220x300.jpg 220w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Find the sum.<br \/>\nQuestion 15.<br \/>\n\\(\\sum_{n=1}^{9}\\)(3n + 5)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/06\/d823a044b03d39a731df3ad26995ae3a\/c7402130b20e29dda11979f913b1f1b1\/lateximg.png?tcb=1622022745\" \/><\/p>\n<p>Question 16.<br \/>\n\\(\\sum_{k=1}^{5}\\)11(\u22123)<sup>k\u22122<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/06\/e36903ae338efa954036f432848755d7\/56d05a52188953f900d43182263e7f44\/lateximg.png?tcb=1622022760\" \/><\/p>\n<p>Question 17.<br \/>\n\\(\\sum_{i=1}^{12}\\)\u22124 (\\(\\frac{1}{2}\\))<sup>i+3<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/06\/106e53fdb8f011b07707cd2ca6682427\/1774252e58e9d2908e8919109d5896f1\/lateximg.png?tcb=1622022773\" \/><\/p>\n<p>Question 18.<br \/>\nPieces of chalk are stacked in a pile. Part of the pile is shown. The bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. Each row has one less piece of chalk than the row below it. How many pieces of chalk are in the pile?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38681\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-8-Sequences-and-Series-q-4.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 8 Sequences and Series q 4\" width=\"298\" height=\"138\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/04\/06\/b917a83c1d0a7b142558402e6b8b9f70\/0a7350466197a65d23ffa68ebf5150d6\/lateximg.png?tcb=1622022790\" \/><\/p>\n<p>Question 19.<br \/>\nYou accept a job as an environmental engineer that pays a salary of $45,000 in the first year. After the first year, your salary increases by 3.5% per year.<br \/>\na. Write a rule giving your salary an for your nth year of employment.<br \/>\nb. What will your salary be during your fifth year of employment?<br \/>\nc. You work 10 years for the company. What are your total earnings? Justify your answer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112948\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.19JPG.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.19JPG.jpg\" width=\"582\" height=\"867\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.19JPG.jpg 582w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-quiz-exercise-8.1-8.3-Answer-.19JPG-201x300.jpg 201w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<h3><a id=\"Lesson_8.4_Finding_Sums_of_Infinite_Geometric_Series\"><\/a>Lesson 8.4 Finding Sums of Infinite Geometric Series<\/h3>\n<p><strong>Essential Question<\/strong> How can you find the sum of an infinite geometric series?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding Sums of Infinite Geometric Series<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38682\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 1\" width=\"212\" height=\"237\" \/><br \/>\nWork with a partner. Enter each geometric series in a spreadsheet. Then use the spreadsheet to determine whether the infinite geometric series has a finite sum. If it does, find the sum. Explain your reasoning. (The figure shows a partially completed spreadsheet for part (a).)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38683\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-2.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 2\" width=\"486\" height=\"304\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-2.png 486w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-2-300x188.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing a Conjecture<br \/>\nWork with a partner. Look back at the infinite geometric series in Exploration 1. Write a conjecture about how you can determine whether the infinite geometric series<br \/>\na<sub>1<\/sub> + a<sub>1<\/sub>r + a<sub>1<\/sub>r<sup>2<\/sup> + a<sub>1<\/sub>r<sup>3<\/sup> +. . .has a finite sum.<\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Writing a Formula<br \/>\nWork with a partner. In Lesson 8.3, you learned that the sum of the first n terms of a geometric series with first term a<sub>1<\/sub> and common ratio r\u2260 1 is<br \/>\nS<sub>n<\/sub> = a<sub>1<\/sub>\\(\\left(\\frac{1-r^{n}}{1-r}\\right)\\)<br \/>\nWhen an infinite geometric series has a finite sum, what happens to r n as n increases? Explain your reasoning. Write a formula to find the sum of an infinite geometric series. Then verify your formula by checking the sums you obtained in Exploration 1.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you find the sum of an infinite geometric series?<br \/>\nAnswer:<br \/>\nSum = a1(1 &#8211; r)<br \/>\na1 = first term<br \/>\nr = rate of change<\/p>\n<p>Question 5.<br \/>\nFind the sum of each infinite geometric series, if it exists.<br \/>\na. 1 + 0.1 + 0.01 + 0.001 + 0.0001 +. . .<br \/>\nb. \\(2+\\frac{4}{3}+\\frac{8}{9}+\\frac{16}{27}+\\frac{32}{81}+\\cdots\\)<br \/>\nAnswer:<br \/>\na. 1 + 0.1 + 0.01 + 0.001 + 0.0001 +. . .<br \/>\nGiven,<br \/>\n1 + 0.1 + 0.01 + 0.001 + 0.0001 +. . .<br \/>\na1 = 1<br \/>\n|r| &lt; 1, the series does have a limit given by formula of limit or sum of an infinite geometric series<br \/>\nS\u221e = a1\/1-r<br \/>\nS\u221e = 1\/1 &#8211; 0.1 = 1\/0.9 = 1.11&#8230;<\/p>\n<p>b. \\(2+\\frac{4}{3}+\\frac{8}{9}+\\frac{16}{27}+\\frac{32}{81}+\\cdots\\)<br \/>\nr = a2\/a1<br \/>\nr = 4\/3\/2<br \/>\nr = 2\/3<br \/>\na1 = 2 and r = 2\/3<br \/>\nSn = a1\/1 &#8211; r<br \/>\nS = 2\/(1-2\/3)<br \/>\nS = 6<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nConsider the infinite geometric series<br \/>\n\\(\\frac{2}{5}+\\frac{4}{25}+\\frac{8}{125}+\\frac{16}{1625}+\\frac{32}{3125}+\\cdots\\)<br \/>\nFind and graph the partial sums S<sub>n<\/sub> for n = 1, 2, 3, 4, and 5. Then describe what happens to S<sub>n<\/sub> as n increases.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112956\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-1.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-1.jpg\" width=\"656\" height=\"662\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-1.jpg 656w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-1-297x300.jpg 297w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-1-150x150.jpg 150w\" sizes=\"(max-width: 656px) 100vw, 656px\" \/><\/p>\n<p><strong>Find the sum of the infinite geometric series, if it exists.<\/strong><br \/>\nQuestion 2.<br \/>\n\\(\\sum_{n=1}^{\\infty}\\left(-\\frac{1}{2}\\right)^{n-1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112958\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-2.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-2.jpg\" width=\"407\" height=\"347\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-2.jpg 407w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-2-300x256.jpg 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>Question 3.<br \/>\n\\(\\sum_{n=1}^{\\infty} 3\\left(\\frac{5}{4}\\right)^{n-1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112959\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-3.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-3.jpg\" width=\"389\" height=\"232\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-3.jpg 389w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-3-300x179.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 4.<br \/>\n\\(3+\\frac{3}{4}+\\frac{3}{16}+\\frac{3}{64}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113512\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-4.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-4.jpg\" width=\"404\" height=\"337\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-4.jpg 404w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-4-300x250.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p>Question 5.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 3, suppose the pendulum travels 10 inches on its first swing. What is the total distance the pendulum swings?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113513\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-5.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-5.jpg\" width=\"389\" height=\"225\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-5.jpg 389w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-5-300x174.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p><strong>Write the repeating decimal as a fraction in simplest form.<\/strong><br \/>\nQuestion 6.<br \/>\n0.555 . . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113514\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-6.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-6.jpg\" width=\"389\" height=\"265\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-6.jpg 389w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-6-300x204.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 7.<br \/>\n0.727272 . . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113515\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-7.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-7.jpg\" width=\"399\" height=\"298\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-7.jpg 399w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-7-300x224.jpg 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>Question 8.<br \/>\n0.131313 . . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-8.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.4-Answer-8.jpg\" \/><\/p>\n<h3><a id=\"Finding_Sums_of_Infinite_Geometric_Series_8.4_Exercises\"><\/a>Finding Sums of Infinite Geometric Series 8.4 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe sum S<sub>n<\/sub> of the first n terms of an infinite series is called a(n) ________.<br \/>\nAnswer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45744\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 1\" width=\"571\" height=\"60\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-1.png 571w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-1-300x32.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to tell whether the series \\(\\sum_{i=1}^{\\infty}\\)a<sub>1<\/sub>r<sup>i\u22121<\/sup> has a sum.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/09\/65112c0113dab4c69f790d3f2207d02b\/0323c5f2e9f70160d02e598911c5853e\/lateximg.png?tcb=1622045956\" width=\"338\" height=\"75\" \/><\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p>In Exercises 3\u20136, consider the infinite geometric series. Find and graph the partial sums S<sub>n<\/sub> for n= 1, 2, 3, 4, and 5. Then describe what happens to S<sub>n<\/sub> as n increases.<br \/>\nQuestion 3.<br \/>\n\\(\\frac{1}{2}+\\frac{1}{6}+\\frac{1}{18}+\\frac{1}{54}+\\frac{1}{162}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45745\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 3\" width=\"455\" height=\"600\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-3.png 455w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-3-228x300.png 228w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{2}{3}+\\frac{1}{3}+\\frac{1}{6}+\\frac{1}{12}+\\frac{1}{24}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113517\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-4.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-4.jpg\" width=\"504\" height=\"534\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-4.jpg 504w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-4-283x300.jpg 283w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<p>Question 5.<br \/>\n4 + \\(\\frac{12}{5}+\\frac{36}{25}+\\frac{108}{125}+\\frac{324}{625}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45746\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-5.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 5\" width=\"453\" height=\"538\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-5.png 453w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-5-253x300.png 253w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Question 6.<br \/>\n2 + \\(\\frac{2}{6}+\\frac{2}{36}+\\frac{2}{216}+\\frac{2}{1296}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113518\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-6.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-6.jpg\" width=\"573\" height=\"630\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-6.jpg 573w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-6-273x300.jpg 273w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p><strong>In Exercises 7\u201314, find the sum of the infinite geometric series, if it exists.<\/strong><br \/>\nQuestion 7.<br \/>\n\\(\\sum_{n=1}^{\\infty} 8\\left(\\frac{1}{5}\\right)^{n-1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45747\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-7.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 7\" width=\"555\" height=\"241\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-7.png 555w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-7-300x130.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\sum_{k=1}^{\\infty}-6\\left(\\frac{3}{2}\\right)^{k-1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/09\/c1402d8541287d32035e8ffcf6ac7564\/72d53b00e49d1f305b9e72865b85ee49\/lateximg.png?tcb=1622046302\" \/><\/p>\n<p>Question 9.<br \/>\n\\(\\sum_{k=1}^{\\infty} \\frac{11}{3}\\left(\\frac{3}{8}\\right)^{k-1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45748\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-9.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 9\" width=\"568\" height=\"293\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-9.png 568w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-9-300x155.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\sum_{i=1}^{\\infty} \\frac{2}{5}\\left(\\frac{5}{3}\\right)^{i-1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/09\/99194740c361556c0bc1d5ca604ad779\/0a9bc24329d246bb8372d31514815bd3\/lateximg.png?tcb=1622046328\" \/><\/p>\n<p>Question 11.<br \/>\n2 + \\(\\frac{6}{4}+\\frac{18}{16}+\\frac{54}{64}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45749\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-11.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 11\" width=\"576\" height=\"233\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-11.png 576w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-11-300x121.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 12.<br \/>\n-5 &#8211; 2 &#8211; \\(\\frac{4}{5}-\\frac{8}{25}-\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/29\/7ed19df6dea5dd5f7a85302a28e7315b\/fe3494433bf81bcded1b2bc4be44c2c5\/lateximg.png?tcb=1622046353\" \/><\/p>\n<p>Question 13.<br \/>\n3 + \\(\\frac{5}{2}+\\frac{25}{12}+\\frac{125}{72}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45751\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-13.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 13\" width=\"585\" height=\"237\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-13.png 585w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-13-300x122.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 14.<br \/>\n\\(\\frac{1}{2}-\\frac{5}{3}+\\frac{50}{9}-\\frac{500}{27}+\\cdots\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/09\/67c5f7eb74aff93406e872fab86dde2f\/2cbb74b8c7492a4e4f91b169c6594c43\/lateximg.png?tcb=1622046381\" \/><\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 15 and 16, describe and correct the error in finding the sum of the infinite geometric series.<br \/>\nQuestion 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38684\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 3\" width=\"323\" height=\"164\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-3.png 323w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-3-300x152.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45752\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-15.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 15\" width=\"388\" height=\"49\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-15.png 388w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-15-300x38.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38685\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-4.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 4\" width=\"324\" height=\"170\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-4.png 324w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-4-300x157.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/29\/66c5c6fbeefb2e664ee724ff000ee8ae\/6d656a1890ddece69a9bad5ddff8298d\/lateximg.png?tcb=1622046408\" \/><\/p>\n<p>Question 17.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou push your younger cousin on a tire swing one time and then allow your cousin to swing freely. On the first swing, your cousin travels a distance of 14 feet. On each successive swing, your cousin travels 75% of the distance of the previous swing. What is the total distance your cousin swings?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38686\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-5.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 5\" width=\"344\" height=\"98\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-5.png 344w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-5-300x85.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45753\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-17.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 17\" width=\"567\" height=\"269\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-17.png 567w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-17-300x142.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA company had a profit of $350,000 in its first year. Since then, the company\u2019s profit has decreased by 12% per year. Assuming this trend continues, what is the total profit the company can make over the course of its lifetime? Justify your answer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/29\/22e90ab7c0a66f416e4fa8284ead1cf7\/bc010828d0a0bb1d0dbd902cf1237ac7\/lateximg.png?tcb=1622046436\" \/><\/p>\n<p><strong>In Exercises 19\u201324, write the repeating decimal as a fraction in simplest form.<\/strong><br \/>\nQuestion 19.<br \/>\n0.222 . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45754\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-19.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 19\" width=\"557\" height=\"329\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-19.png 557w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-19-300x177.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 20.<br \/>\n0.444 . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/29\/47f1c613e0f60dfecf176a2a8da0f546\/c3e63f7ae0eb02cbb78ee10c86b36b78\/lateximg.png?tcb=1622046462\" \/><\/p>\n<p>Question 21.<br \/>\n0.161616 . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45755\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-21.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 21\" width=\"570\" height=\"328\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-21.png 570w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-21-300x173.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 22.<br \/>\n0.625625625 . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/29\/7d592208c0d648078f17775223a7d517\/92a704913cbb1f3c6853a4fd11c91a68\/lateximg.png?tcb=1622046488\" \/><\/p>\n<p>Question 23.<br \/>\n32.323232 . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45756\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-23.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 23\" width=\"568\" height=\"383\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-23.png 568w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-23-300x202.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 24.<br \/>\n130.130130130 . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/29\/0d33c81afdf77255580dbbf3c21c48f7\/f3f5d3803a56dda7877b7438ec348af1\/lateximg.png?tcb=1622046514\" \/><\/p>\n<p>Question 25.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nFind two infinite geometric series whose sums are each 6. Justify your answers.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45757\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-25.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 25\" width=\"479\" height=\"313\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-25.png 479w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-25-300x196.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph shows the partial sums of the geometric series a<sub>1<\/sub> + a<sub>2<\/sub> + a<sub>3<\/sub> + a<sub>4<\/sub>+. . . .What is the value of \\(\\sum_{n=1}^{\\infty}\\)a<sub>n<\/sub> ? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38687\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-6.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 6\" width=\"145\" height=\"146\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/29\/1a14e268581f887be5b20bf111ee0da9\/4cc32e3fe919a7eb738d592dbfdeaa97\/lateximg.png?tcb=1622046538\" \/><\/p>\n<p>Question 27.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA radio station has a daily contest in which a random listener is asked a trivia question. On the first day, the station gives $500 to the first listener who answers correctly. On each successive day, the winner receives 90% of the winnings from the previous day. What is the total amount of prize money the radio station gives away during the contest?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45758\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-27.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 27\" width=\"574\" height=\"214\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-27.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-27-300x112.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nArchimedes used the sum of a geometric series to compute the area enclosed by a parabola and a straight line. In \u201cQuadrature of the Parabola,\u201d he proved that the area of the region is \\(\\frac{4}{3}\\) the area of the inscribed triangle. The first term of the series for the parabola below is represented by the area of the blue triangle and the second term is represented by the area of the red triangles. Use Archimedes\u2019 result to find the area of the region. Then write the area as the sum of an infinite geometric series.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38688\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-7.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 7\" width=\"223\" height=\"178\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113522\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-28.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-28.jpg\" width=\"584\" height=\"916\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-28.jpg 584w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-28-191x300.jpg 191w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 29.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nCan a person running at 20 feet per second ever catch up to a tortoise that runs 10 feet per second when the tortoise has a 20-foot head start? The Greek mathematician Zeno said no. He reasoned as follows:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38689\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-8.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 8\" width=\"334\" height=\"157\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-8.png 334w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-8-300x141.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\nLooking at the race as Zeno did, the distances and the times it takes the person to run those distances both form infinite geometric series. Using the table, show that both series have finite sums. Does the person catch up to the tortoise? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38690\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-9.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 9\" width=\"326\" height=\"75\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-9.png 326w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-9-300x69.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45759\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-29.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 29\" width=\"566\" height=\"346\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-29.png 566w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-29-300x183.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that 0.999 . . . is equal to 1. Is your friend correct? Justify your answer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/4fa5134872e872db009581ac0323fa82\/e7c85b3bea20bd0d32f76ecd105ce76e\/lateximg.png?tcb=1622046764\" \/><\/p>\n<p>Question 31.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe Sierpinski triangle is a fractal created using equilateral triangles. The process involves removing smaller triangles from larger triangles by joining the midpoints of the sides of the larger triangles as shown. Assume that the initial triangle has an area of 1 square foot.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38691\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-10.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 10\" width=\"291\" height=\"84\" \/><br \/>\na. Let an be the total area of all the triangles that are removed at Stage n. Write a rule for a<sub>n<\/sub>.<br \/>\nb. Find \\(\\sum_{n=1}^{\\infty}\\)a<sub>n<\/sub>. Interpret your answer in the context of this situation.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45760\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-31.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 31\" width=\"603\" height=\"364\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-31.png 603w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-31-300x181.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Determine the type of function represented by the table.<\/strong><br \/>\nQuestion 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38692\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-11.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 11\" width=\"263\" height=\"71\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113523\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-32.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-32.jpg\" width=\"596\" height=\"526\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-32.jpg 596w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-exercise-8.4-Answer-32-300x265.jpg 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/p>\n<p>Question 33.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38693\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-12.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 12\" width=\"264\" height=\"73\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45761\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-33.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 33\" width=\"577\" height=\"218\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-33.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-33-300x113.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p><strong>Determine whether the sequence is arithmetic, geometric, or neither.<\/strong><br \/>\nQuestion 34.<br \/>\n\u22127, \u22121, 5, 11, 17, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/5093ae119be0075417faac4241acea4a\/dd534b8eb4f355fdf33287247c327c7f\/lateximg.png?tcb=1622046914\" \/><\/p>\n<p>Question 35.<br \/>\n0, \u22121, \u22123, \u22127, \u221215, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45762\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-35.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 8 Sequences and Series 8.4 a 35\" width=\"468\" height=\"99\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-35.png 468w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-8-Sequences-and-Series-8.4-a-35-300x63.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 36.<br \/>\n13.5, 40.5, 121.5, 364.5, . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/59de3c395faee80182a21035b5d3abbb\/5531b2f26f6050438d10b852eeadda2d\/lateximg.png?tcb=1622046942\" \/><\/p>\n<h3><a id=\"Lesson_8.5_Using_Recursive_Rules_with_Sequences\"><\/a>Lesson 8.5 Using Recursive Rules with Sequences<\/h3>\n<p><strong>Essential Question<\/strong> How can you define a sequence recursively? A recursive rule gives the beginning term(s) of a sequence and a recursive equation that tells how a<sub>n<\/sub> is related to one or more preceding terms.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Evaluating a Recursive Rule<br \/>\nWork with a partner. Use each recursive rule and a spreadsheet to write the first six terms of the sequence. Classify the sequence as arithmetic, geometric, or neither. Explain your reasoning. (The figure shows a partially completed spreadsheet for part (a).)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38694\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 1\" width=\"501\" height=\"217\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-1.png 501w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-1-300x130.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing a Recursive Rule<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38695\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-2.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 2\" width=\"224\" height=\"133\" \/><br \/>\nWork with a partner. Write a recursive rule for the sequence. Explain your reasoning.<br \/>\na. 3, 6, 9, 12, 15, 18, . . .<br \/>\nb. 18, 14, 10, 6, 2, \u22122, . . .<br \/>\nc. 3, 6, 12, 24, 48, 96, . . .<br \/>\nd. 128, 64, 32, 16, 8, 4, . . .<br \/>\ne. 5, 5, 5, 5, 5, 5, . . .<br \/>\nf. 1, 1, 2, 3, 5, 8, . . .<\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Writing a Recursive RuleWork with a partner. Write a recursive rule for the sequence whose graph is shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38696\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-3.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 3\" width=\"470\" height=\"148\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-3.png 470w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-3-300x94.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you define a sequence recursively?<br \/>\nAnswer: A recursive sequence is a sequence in which terms are defined using one or more previous terms.<\/p>\n<p>Question 5.<br \/>\nWrite a recursive rule that is different from those in Explorations 1\u20133. Write the first six terms of the sequence. Then graph the sequence and classify it as arithmetic, geometric, or neither.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Write the first six terms of the sequence.<\/strong><br \/>\nQuestion 1.<br \/>\na<sub>1<\/sub> = 3, a<sub>n<\/sub> = a<sub>n-1<\/sub> \u2212 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113529\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-1.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-1.jpg\" width=\"282\" height=\"180\" \/><\/p>\n<p>Question 2.<br \/>\na<sub>0<\/sub> = 162, a<sub>n<\/sub> = 0.5a<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113530\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-2.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-2.jpg\" width=\"268\" height=\"175\" \/><\/p>\n<p>Question 3.<br \/>\nf(0) = 1, f(n) = f(n\u2212 1) + n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113531\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-3.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-3.jpg\" width=\"252\" height=\"164\" \/><\/p>\n<p>Question 4.<br \/>\na<sub>1<\/sub> = 4, a<sub>n<\/sub> = 2a<sub>n-1<\/sub> \u2212 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113532\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-4.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-4.jpg\" width=\"274\" height=\"174\" \/><\/p>\n<p><strong>Write a recursive rule for the sequence.<\/strong><br \/>\nQuestion 5.<br \/>\n2, 14, 98, 686, 4802, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113535\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-5.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-5.jpg\" width=\"197\" height=\"187\" \/><\/p>\n<p>Question 6.<br \/>\n19, 13, 7, 1, \u22125, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113537\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-6.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-6.jpg\" width=\"214\" height=\"139\" \/><\/p>\n<p>Question 7.<br \/>\n11, 22, 33, 44, 55, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113538\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-7.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-7.jpg\" width=\"221\" height=\"145\" \/><\/p>\n<p>Question 8.<br \/>\n1, 2, 2, 4, 8, 32, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113539\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-8.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-8.jpg\" width=\"157\" height=\"153\" \/><\/p>\n<p><strong>Write a recursive rule for the sequence.<\/strong><br \/>\nQuestion 9.<br \/>\na<sub>n<\/sub> = 17 \u2212 4n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113540\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-9.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-9.jpg\" width=\"307\" height=\"121\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-9.jpg 307w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-9-300x118.jpg 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Question 10.<br \/>\na<sub>n<\/sub> = 16(3)<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113541\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-10.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-10.jpg\" width=\"298\" height=\"106\" \/><\/p>\n<p><strong>Write an explicit rule for the sequence.<\/strong><br \/>\nQuestion 11.<br \/>\na<sub>1<\/sub> = \u221212, a<sub>n<\/sub> = a<sub>n-1<\/sub> + 16<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113542\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-11.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-11.jpg\" width=\"357\" height=\"189\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-11.jpg 357w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-11-300x159.jpg 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p>Question 12.<br \/>\na<sub>1<\/sub> = 2, a<sub>n<\/sub> = \u22126a<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113543\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-12.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-12.jpg\" width=\"270\" height=\"191\" \/><\/p>\n<p>Question 13.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 6, suppose 75% of the fish remain each year. What happens to the population of fish over time?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113544\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-13.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-13.jpg\" width=\"463\" height=\"416\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-13.jpg 463w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-13-300x270.jpg 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/p>\n<p>Question 14.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nHow do the answers in Example 7 change when the annual interest rate is 7.5% and the monthly payment is $1048.82?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113545\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-14.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-14.jpg\" width=\"458\" height=\"666\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-14.jpg 458w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Monitoring-progress-exercise-8.5-Answer-14-206x300.jpg 206w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><\/p>\n<h3><a id=\"Using_Recursive_Rules_with_Sequences_8.5_Exercises\"><\/a>Using Recursive Rules with Sequences 8.5 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nA recursive _________ tells how the nth term of a sequence is related to one or more preceding terms.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45763\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 1\" width=\"557\" height=\"55\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-1.png 557w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-1-300x30.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain the difference between an explicit rule and a recursive rule for a sequence.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/10\/d43c9a2fa143922a0f8fc031e05c6be4\/be5806c623180e5f4e8c520b94c8a404\/lateximg.png?tcb=1622050868\" \/><\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, write the first six terms of the sequence.<\/strong><br \/>\nQuestion 3.<br \/>\na<sub>1<\/sub> = 1<br \/>\na<sub>n<\/sub> = a<sub>n-1<\/sub> + 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45764\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-3.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 3\" width=\"275\" height=\"209\" \/><\/p>\n<p>Question 4.<br \/>\na<sub>1<\/sub> = 1<br \/>\na<sub>n<\/sub> = a<sub>n-1<\/sub> \u2212 5<br \/>\nAnswer:<br \/>\na<sub>1<\/sub> = 1<br \/>\na<sub>n<\/sub> = a<sub>n-1<\/sub> \u2212 5<br \/>\na2 = a1 &#8211; 5 = 1-5 = -4<br \/>\na3 = a2 &#8211; 5 = -4 &#8211; 5 = -9<br \/>\na4 = a3 &#8211; 5 = -9 &#8211; 5 = -14<br \/>\na5 = a4 &#8211; 5 = -14 &#8211; 5 = -19<br \/>\na6 = a5 &#8211; 5 = -19 &#8211; 5 = -24<br \/>\nThus the first six terms of the sequence are 1, -4, -9, -14, -19, -24<\/p>\n<p>Question 5.<br \/>\nf(0) = 4<br \/>\nf(n) = 2f (n\u2212 1)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45765\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-5.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 5\" width=\"271\" height=\"204\" \/><\/p>\n<p>Question 6.<br \/>\nf(0) = 10<br \/>\nf(n) = \\(\\frac{1}{2}\\)f(n\u2212 1)<br \/>\nAnswer:<br \/>\nf(0) = 10<br \/>\nf(n) = \\(\\frac{1}{2}\\)f(n\u2212 1)<br \/>\nf(1) = \\(\\frac{1}{2}\\)f(0) = 1\/2 \u00d7 10 = 5<br \/>\nf(2) = \\(\\frac{1}{2}\\)f(1) = 1\/2 \u00d7 5 = 5\/2<br \/>\nf(3) = \\(\\frac{1}{2}\\)f(2) = 1\/2 \u00d7 5\/2 = 5\/4<br \/>\nf(4) = \\(\\frac{1}{2}\\)f(3) = 1\/2 \u00d7 5\/4 = 5\/8<br \/>\nf(5) = \\(\\frac{1}{2}\\)f(4) = 1\/2 \u00d7 5\/8 = 5\/16<br \/>\nThus the first six terms of the sequence are 10, 5, 5\/2, 5\/4, 5\/8, 5\/16,&#8230;<\/p>\n<p>Question 7.<br \/>\na<sub>1<\/sub> = 2<br \/>\na<sub>n<\/sub> = (a<sub>n-1<\/sub>)<sup>2<\/sup> + 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45766\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-7.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 7\" width=\"481\" height=\"207\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-7.png 481w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-7-300x129.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 8.<br \/>\na<sub>1<\/sub> = 1<br \/>\na<sub>n<\/sub> = (a<sub>n-1<\/sub>)<sup>2<\/sup> \u2212 10<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/10\/a53b873d2dded288ffb95c29c9cb212a\/b2d705ad4c515b4864b1ad0ad445d546\/lateximg.png?tcb=1622051576\" \/><\/p>\n<p>Question 9.<br \/>\nf(0) = 2, f (1) = 4<br \/>\nf(n) = f(n \u2212 1) \u2212 f(n \u2212 2)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45767\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-9.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 9\" width=\"372\" height=\"206\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-9.png 372w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-9-300x166.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><\/p>\n<p>Question 10.<br \/>\nf(1) = 2, f(2) = 3<br \/>\nf(n) = f(n \u2212 1) \u2022 f(n \u2212 2)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/10\/5ef33f7664eb81f4ed4aa0b32183c714\/1d412552d7bdc7a45bdb234450cb7926\/lateximg.png?tcb=1622051550\" \/><\/p>\n<p><strong>In Exercises 11\u201322, write a recursive rule for the sequence.<\/strong><br \/>\nQuestion 11.<br \/>\n21, 14, 7, 0, \u22127, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45768\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-11.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 11\" width=\"551\" height=\"300\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-11.png 551w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-11-300x163.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 12.<br \/>\n54, 43, 32, 21, 10, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/d028e79f898f15738d4b5c1153ae5c33\/da080c93a8b118d0dd48a9c4fb1e189c\/lateximg.png?tcb=1622051509\" \/><\/p>\n<p>Question 13.<br \/>\n3, 12, 48, 192, 768, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45769\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-13.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 13\" width=\"578\" height=\"300\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-13.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-13-300x156.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 14.<br \/>\n4, \u221212, 36, \u2212108, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/ee2a3f78d989952e13bc689d21a4295c\/2d597e10ad0dd8fb73bec706096031d9\/lateximg.png?tcb=1622051483\" \/><\/p>\n<p>Question 15.<br \/>\n44, 11, \\(\\frac{11}{4}\\), \\(\\frac{11}{16}\\), \\(\\frac{11}{64}\\), . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45770\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-15.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 15\" width=\"534\" height=\"391\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-15.png 534w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-15-300x220.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 16.<br \/>\n1, 8, 15, 22, 29, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/332d15841b96a78cfd7497bb96e852f7\/49a76c11a512b5d18c752a2a6234a0df\/lateximg.png?tcb=1622051349\" \/><\/p>\n<p>Question 17.<br \/>\n2, 5, 10, 50, 500, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45771\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-17.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 17\" width=\"578\" height=\"120\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-17.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-17-300x62.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 18.<br \/>\n3, 5, 15, 75, 1125, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/1f017e089dadf010abee63900ecf08c4\/c47958ac51e218ce476411d650512b0f\/lateximg.png?tcb=1622051325\" \/><\/p>\n<p>Question 19.<br \/>\n1, 4, 5, 9, 14, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45772\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-19.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 19\" width=\"572\" height=\"150\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-19.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-19-300x79.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 20.<br \/>\n16, 9, 7, 2, 5, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/31983154d590876a32ef67eab476139e\/0fa573edb597d80465b72530969bcacd\/lateximg.png?tcb=1622051300\" \/><\/p>\n<p>Question 21.<br \/>\n6, 12, 36, 144, 720, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45773\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-21.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 21\" width=\"560\" height=\"121\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-21.png 560w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-21-300x65.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 22.<br \/>\n\u22123, \u22121, 2, 6, 11, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/0da4ce8a03fa9d122047667c46bd0a3e\/8ec129420e131ab829c067d8ef3bf135\/lateximg.png?tcb=1622051274\" \/><\/p>\n<p><strong>In Exercises 23\u201326, write a recursive rule for the sequence shown in the graph.<\/strong><br \/>\nQuestion 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38697\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-4.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 4\" width=\"106\" height=\"111\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45774\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-23.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 23\" width=\"572\" height=\"332\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-23.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-23-300x174.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38698\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-5.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 5\" width=\"107\" height=\"108\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/7f8be1e0eb778982a6051e6cb654da78\/f6329d3ede67926cc0a2a1bd52bdda69\/lateximg.png?tcb=1622051248\" \/><\/p>\n<p>Question 25.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38699\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-6.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 6\" width=\"119\" height=\"100\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45775\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-25.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 25\" width=\"535\" height=\"364\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-25.png 535w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-25-300x204.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 26.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38700\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-7.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 7\" width=\"115\" height=\"107\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/2118dcb78c9e9e03900a4456efc77d82\/2a44f0a9bf03ae174c5a538cee942036\/lateximg.png?tcb=1622051222\" \/><\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 27 and 28, describe and correct the error in writing a recursive rule for the sequence 5, 2, 3, -1, 4, . . ..<br \/>\nQuestion 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38701\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-8.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 8\" width=\"317\" height=\"150\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-8.png 317w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-8-300x142.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45776\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-27.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 27\" width=\"568\" height=\"67\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-27.png 568w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-27-300x35.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 28.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38702\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-9.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 9\" width=\"319\" height=\"149\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-9.png 319w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-9-300x140.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/10\/d9f9616f7b7486364f03dcc3cc5bc1da\/d277425cf765ab317d44b10cb5c5201d\/lateximg.png?tcb=1622051190\" \/><\/p>\n<p><strong>In Exercises 29\u201338, write a recursive rule for the sequence.<\/strong><br \/>\nQuestion 29.<br \/>\na<sub>n<\/sub> = 3 + 4n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45777\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-29.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 29\" width=\"573\" height=\"169\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-29.png 573w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-29-300x88.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 30.<br \/>\na<sub>n<\/sub> =\u22122 \u2212 8n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/c29a938e263c3d53e62b6368aae58896\/0ae543666e8241c93ff8f99fc2679c30\/lateximg.png?tcb=1622051160\" \/><\/p>\n<p>Question 31.<br \/>\na<sub>n<\/sub> = 12 \u2212 10n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45778\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-31.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 31\" width=\"569\" height=\"172\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-31.png 569w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-31-300x91.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 32.<br \/>\na<sub>n<\/sub> = 9 \u2212 5n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/b800c4a037485d3efd1ffd2e57ab3c32\/e08acbf1a8de355fc06296bb2cc334da\/lateximg.png?tcb=1622051136\" \/><\/p>\n<p>Question 33.<br \/>\na<sub>n<\/sub> = 12(11)<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45779\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-33.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 33\" width=\"564\" height=\"167\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-33.png 564w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-33-300x89.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 34.<br \/>\na<sub>n<\/sub> = \u22127(6)<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/92d8849cc18480bc9c800d99fc485a18\/69316f66a009df0dd92224f092702598\/lateximg.png?tcb=1622051108\" \/><\/p>\n<p>Question 35.<br \/>\na<sub>n<\/sub> = 2.5 \u2212 0.6n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45780\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-35.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 35\" width=\"570\" height=\"193\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-35.png 570w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-35-300x102.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 36.<br \/>\na<sub>n<\/sub> = \u22121.4 + 0.5n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/ff30a30478f23437db14ed0a986eab98\/979250602e6d8f1ab80cae6e16967f8f\/lateximg.png?tcb=1622051075\" \/><\/p>\n<p>Question 37.<br \/>\na<sub>n<\/sub>= \u2212\\(\\frac{1}{2}\\left(\\frac{1}{4}\\right)^{n-1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45781\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-37.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 37\" width=\"557\" height=\"190\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-37.png 557w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-37-300x102.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 38.<br \/>\na<sub>n<\/sub> = \\(\\frac{1}{4}\\)(5)<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/080cacfb48a3ec502a382d85f8beb27c\/bdefff72e70b37a5dfdea2982b5be3e1\/lateximg.png?tcb=1622051048\" \/><\/p>\n<p>Question 39.<br \/>\n<strong>REWRITING A FORMULA<\/strong><br \/>\nYou have saved $82 to buy a bicycle. You save an additional $30 each month. The explicit rule an= 30n+ 82 gives the amount saved after n months. Write are cursive rule for the amount you have saved n months from now.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38703\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-10.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 10\" width=\"184\" height=\"159\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45782\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-39.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 39\" width=\"585\" height=\"198\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-39.png 585w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-39-300x102.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>REWRITING A FORMULA<\/strong><br \/>\nYour salary is given by the explicit rule a<sub>n<\/sub> = 35,000(1.04)<sub>n-1<\/sub>, where n is the number of years you have worked. Write a recursive rule for your salary.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/829e81a4f358dad1bbcb1d99e1704377\/6f14a9aa1cb3ef23e9ea15f2ca4992bb\/lateximg.png?tcb=1622051017\" \/><\/p>\n<p><strong>In Exercises 41\u201348, write an explicit rule for the sequence.<\/strong><br \/>\nQuestion 41.<br \/>\na<sub>1<\/sub> = 3, a<sub>n<\/sub> = a<sub>n-1<\/sub> \u2212 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45783\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-41.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 41\" width=\"577\" height=\"203\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-41.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-41-300x106.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 42.<br \/>\na<sub>1<\/sub> = 16, a<sub>n<\/sub> = a<sub>n-1<\/sub> + 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/30\/f7dddde2e58cd911a5059aea27c0be11\/2ae9905d0878be312fef2c15b9fab8a2\/lateximg.png?tcb=1622050990\" \/><\/p>\n<p>Question 43.<br \/>\na<sub>1<\/sub> = \u22122, a<sub>n<\/sub> = 3a<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45784\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-43.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 43\" width=\"559\" height=\"167\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-43.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-43-300x90.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 44.<br \/>\na<sub>1<\/sub> = 13, a<sub>n<\/sub> = 4a<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/31\/336cfa54fc2c356f728156b50781d495\/311b7164fec4ffc986a4fa10d95fbd25\/lateximg.png?tcb=1622050963\" \/><\/p>\n<p>Question 45.<br \/>\na<sub>1<\/sub> = \u221212, a<sub>n<\/sub> = a<sub>n-1<\/sub> + 9.1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45785\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-45.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 45\" width=\"577\" height=\"203\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-45.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-45-300x106.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 46.<br \/>\na<sub>1<\/sub> = \u22124, a<sub>n<\/sub> = 0.65a<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/31\/7742a4e2fbc6f4e6145521e46d7cbac2\/37990de42863e81b7d3184cbb6af5298\/lateximg.png?tcb=1622050924\" \/><\/p>\n<p>Question 47.<br \/>\na<sub>n<\/sub> = 5, a<sub>n<\/sub> = a<sub>n-1<\/sub> \u2212 \\(\\frac{1}{3}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45786\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-47.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 47\" width=\"537\" height=\"212\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-47.png 537w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-47-300x118.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 48.<br \/>\na<sub>1<\/sub> = \u22125, a<sub>n<\/sub> = \\(\\frac{1}{4}\\)a<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/31\/6782779576c99710e6e29b4a28452e72\/c96cc5b912c74420527af942ae2a0775\/lateximg.png?tcb=1622051634\" \/><\/p>\n<p>Question 49.<br \/>\n<strong>REWRITING A FORMULA<\/strong><br \/>\nA grocery store arranges cans in a pyramid-shaped display with 20 cans in the bottom row and two fewer cans in each subsequent row going up. The number of cans in each row is represented by the recursive rule a<sub>1<\/sub> = 20, a<sub>n<\/sub> = a<sub>n-1<\/sub> \u2212 2. Write an explicit rule for the number of cans in row n.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45787\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-49.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 49\" width=\"575\" height=\"224\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-49.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-49-300x117.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>REWRITING A FORMULA<\/strong><br \/>\nThe value of a car is given by the recursive rule a<sub>1<\/sub> = 25,600, a<sub>n<\/sub> = 0.86a<sub>n-1<\/sub>, where n is the number of years since the car was new. Write an explicit rule for the value of the car after n years.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/31\/f5faa4f7f36177f09e44fa27cfe327a2\/22e7cf314e6a90df86dd0d446abde0b9\/lateximg.png?tcb=1622051661\" \/><\/p>\n<p>Question 51.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nWhat is the 1000th term of the sequence whose first term is a<sub>1<\/sub> = 4 and whose nth term is a<sub>n<\/sub> = a<sub>n-1<\/sub> + 6? Justify your answer.<br \/>\nA. 4006<br \/>\nB. 5998<br \/>\nC. 1010<br \/>\nD. 10,000<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45788\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-51.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 51\" width=\"578\" height=\"195\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-51.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-51-300x101.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nWhat is the 873rd term of the sequence whose first term is a<sub>1<\/sub> = 0.01 and whose nth term is a<sub>n<\/sub> = 1.01a<sub>n-1<\/sub>? Justify your answer.<br \/>\nA. 58.65<br \/>\nB. 8.73<br \/>\nC. 1.08<br \/>\nD. 586,459.38<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/31\/6b001ca43316559a067e7f56881a10bc\/8be59b1e69eb4f3bf98f991315a484b9\/lateximg.png?tcb=1622051686\" \/><\/p>\n<p>Question 53.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nAn online music service initially has 50,000 members. Each year, the company loses 20% of its current members and gains 5000 new members.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38704\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-11.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 11\" width=\"299\" height=\"231\" \/><br \/>\na. Write a recursive rule for the number an of members at the start of the nth year.<br \/>\nb. Find the number of members at the start of the fifth year.<br \/>\nc. Describe what happens to the number of members over time.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45789\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-53.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 53\" width=\"593\" height=\"457\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-53.png 593w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-53-300x231.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou add chlorine to a swimming pool. You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. Each week, 40% of the chlorine in the pool evaporates.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38705\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-12.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 12\" width=\"319\" height=\"115\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-12.png 319w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-12-300x108.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\na. Write a recursive rule for the amount of chlorine in the pool at the start of the nth week.<br \/>\nb. Find the amount of chlorine in the pool at the start of the third week.<br \/>\nc. Describe what happens to the amount of chlorine in the pool over time.<br \/>\nAnswer:<br \/>\nGiven that, You add chlorine to a swimming pool. You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. Each week, 40% of the chlorine in the pool evaporates.<br \/>\nWe know that,<br \/>\nan = an-1 + d<br \/>\nan = r . an-1<br \/>\nan = 0.6 \u00d7 an-1 + 16<br \/>\nan = 0.6 \u00d7 an-1 + 16<br \/>\na1 = 34<br \/>\nEnter 340<br \/>\na3 = 16<br \/>\nSo, the amount of chlorine in the pool at the start of the third week is 16.<br \/>\nan = an-1 + d<br \/>\nan = r . an-1<br \/>\nan = 1333<\/p>\n<p>Question 55.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nGive an example of a real-life situation which you can represent with a recursive rule that does not approach a limit. Write a recursive rule that represents the situation.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45790\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-55.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 55\" width=\"549\" height=\"101\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-55.png 549w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-55-300x55.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nGive an example of a sequence in which each term after the third term is a function of the three terms preceding it. Write a recursive rule for the sequence and find its first eight terms.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/03\/31\/de15367e38d8aa13084619a66e9e4477\/0413d9034146706152d501fec727f15b\/lateximg.png?tcb=1622051745\" \/><\/p>\n<p>Question 57.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou borrow $2000 at 9% annual interest compounded monthly for 2 years. The monthly payment is $91.37.<br \/>\na. Find the balance after the fifth payment.<br \/>\nb. Find the amount of the last payment.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45791\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-57.1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 57.1\" width=\"579\" height=\"411\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-57.1.png 579w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-57.1-300x213.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45792\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-57.2.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 57.2\" width=\"592\" height=\"384\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-57.2.png 592w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-57.2-300x195.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou borrow $10,000 to build an extra bedroom onto your house. The loan is secured for 7 years at an annual interest rate of 11.5%. The monthly payment is $173.86.<br \/>\na. Find the balance after the fourth payment.<br \/>\nb. Find the amount of the last payment.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou borrow $10,000 to build an extra bedroom onto your house.<br \/>\nThe loan is secured for 7 years at an annual interest rate of 11.5%.<br \/>\nThe monthly payment is $173.86.<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"399\"><strong>Payment Number<\/strong><\/td>\n<td width=\"399\"><strong>Balance after payment<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"399\">1<\/td>\n<td width=\"399\">9922.14<\/td>\n<\/tr>\n<tr>\n<td width=\"399\">2<\/td>\n<td width=\"399\">9843.53<\/td>\n<\/tr>\n<tr>\n<td width=\"399\">3<\/td>\n<td width=\"399\">9764.17<\/td>\n<\/tr>\n<tr>\n<td width=\"399\">.<\/td>\n<td width=\"399\">.<\/td>\n<\/tr>\n<tr>\n<td width=\"399\">.<\/td>\n<td width=\"399\">.<\/td>\n<\/tr>\n<tr>\n<td width=\"399\">.<\/td>\n<td width=\"399\">.<\/td>\n<\/tr>\n<tr>\n<td width=\"399\">83<\/td>\n<td width=\"399\">186.3<\/td>\n<\/tr>\n<tr>\n<td width=\"399\">84<\/td>\n<td width=\"399\">14.23<\/td>\n<\/tr>\n<tr>\n<td width=\"399\">85<\/td>\n<td width=\"399\">-159.49<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>So that balance after the 4th payment will be = $9684.05 and the balance after 85 payments is 173.86 &#8211; 159.49 = $14.37<\/p>\n<p>Question 59.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nIn 1202, the mathematician Leonardo Fibonacci wrote Liber Abaci, in which he proposed the following rabbit problem:<br \/>\nBegin with a pair of newborn rabbits. When a pair of rabbits is two months old, the rabbits begin producing a new pair of rabbits each month. Assume none of the rabbits die.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38706\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-13.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 13\" width=\"301\" height=\"81\" \/><br \/>\nThis problem produces a sequence called the Fibonacci sequence, which has both a recursive formula and an explicit formula as follows.<br \/>\nRecursive: a<sub>1<\/sub> = 1, a<sub>2<\/sub> = 1, a<sub>n<\/sub> = a<sub>n-2<\/sub> + a<sub>n-1<\/sub><br \/>\nExplicit: f<sub>n<\/sub> = \\(\\frac{1}{\\sqrt{5}}\\left(\\frac{1+\\sqrt{5}}{2}\\right)^{n}-\\frac{1}{\\sqrt{5}}\\left(\\frac{1-\\sqrt{5}}{2}\\right)^{n}\\), n \u2265 1<br \/>\nUse each formula to determine how many rabbits there will be after one year. Justify your answers.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45793\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-59.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 59\" width=\"584\" height=\"268\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-59.png 584w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-59-300x138.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nA town library initially has 54,000 books in its collection. Each year, 2% of the books are lost or discarded. The library can afford to purchase 1150 new books each year.<br \/>\na. Write a recursive rule for the number an of books in the library at the beginning of the nth year.<br \/>\nb. Use the sequence mode and the dot mode of a graphing calculator to graph the sequence. What happens to the number of books in the library over time? Explain.<br \/>\nAnswer:<br \/>\nan = (an-1 \u00d7 0.98) + 1150<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-186557 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Using-Recursive-Rules-with-Sequences-8.5-Exercises_60.png\" alt=\"Big Ideas Math Answers Using Recursive Rules with Sequences 8.5 Exercises_60\" width=\"348\" height=\"337\" \/><\/p>\n<p>Question 61.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nA tree farm initially has 9000 trees. Each year, 10% of the trees are harvested and 800 seedlings are planted.<br \/>\na. Write a recursive rule for the number of trees on the tree farm at the beginning of the nth year.<br \/>\nb. What happens to the number of trees after an extended period of time?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38707\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-14.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 14\" width=\"234\" height=\"160\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45794\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-61.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 61\" width=\"578\" height=\"245\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-61.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-61-300x127.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nYou sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. Sixty percent of the drug is removed from the bloodstream every 8 hours.<br \/>\na. Write a recursive rule for the amount of the drug in the bloodstream after n doses.<br \/>\nb. The value that a drug level approaches after an extended period of time is called the maintenance level. What is the maintenance level of this drug given the prescribed dosage?<br \/>\nc. How does doubling the dosage affect the maintenance level of the drug? Justify your answer.<br \/>\nAnswer:<br \/>\nan = 0.4 an-1 + 325<br \/>\na1 = 325<br \/>\nYou sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days.<br \/>\nSixty percent of the drug is removed from the bloodstream every 8 hours.<br \/>\nwhen n = 30<br \/>\na30 = 0.4(30 &#8211; 1) + 325<br \/>\n= 0.4(29) + 325<br \/>\na30 = 541.66<br \/>\nan = 0.4 an-1 + 650 for n &gt; 1<br \/>\nn = 12<br \/>\n1083.33\/514.6 = 2.105 \u2248 2, the maintenance level doubles when the dose is doubled.<\/p>\n<p>Question 63.<br \/>\n<strong>FINDING A PATTERN<\/strong><br \/>\nA fractal tree starts with a single branch (the trunk). At each stage, each new branch from the previous stage grows two more branches, as\ue031 shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38708\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-15.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 15\" width=\"252\" height=\"180\" \/><br \/>\na. List the number of new branches in each of the first seven stages. What type of sequence do these numbers form?<br \/>\nb. Write an explicit rule and a recursive rule for the sequence in part (a).<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45795\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-63.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 63\" width=\"571\" height=\"298\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-63.png 571w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-63-300x157.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nLet a<sub>1<\/sub> = 34. Then write the terms of the sequence until you discover a pattern.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38709\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-16.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 16\" width=\"243\" height=\"61\" \/><br \/>\nDo the same for a<sub>1<\/sub> = 25. What can you conclude?<br \/>\nAnswer:<br \/>\na1 = 34<br \/>\na1 = 25<br \/>\nan+ 1 = 1\/2 an<br \/>\na1 = 34<br \/>\na 1+1 = 1\/2a1<br \/>\na2 = 1\/2 \u00d7 34 = 17<br \/>\na3 = 1\/2 \u00d7 17 = 8.5<br \/>\na4 = 1\/2 \u00d7 8.5 = 4.25<br \/>\na5 = 1\/2 \u00d7 4.25 = 2.125<br \/>\na6 = 1\/2 \u00d7 2.125 = 1.0625<br \/>\na7 = 1\/2 \u00d7 1.625 = 0.53125<br \/>\na8 = 1\/2 \u00d7 0.53125 = 0.265625<br \/>\nan+1 = 3an + 1<br \/>\na1 = 25<br \/>\na2 = 3a1 + 1<br \/>\na2 = 3 \u00d7 25 + 1 = 76<br \/>\na3 = 3 \u00d7 76 + 1 = 229<br \/>\na4 = 3 \u00d7 229 + 1 = 688<br \/>\na5 = 3 \u00d7 688 + 1 = 2065<br \/>\na6 = 3 \u00d7 2065 + 1 = 6196<\/p>\n<p>Question 65.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou make a $500 down payment on a $3500 diamond ring. You borrow the remaining balance at 10% annual interest compounded monthly. The monthly payment is $213.59. How long does it take to pay back the loan? What is the amount of the last payment? Justify your answers.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45796\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-65.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 65\" width=\"574\" height=\"614\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-65.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-65-280x300.png 280w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 66.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph shows the first six terms of the sequence a<sub>1<\/sub> = p, a<sub>n<\/sub> = ra<sub>n-1<\/sub>.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38710\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-17.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 17\" width=\"170\" height=\"129\" \/><br \/>\na. Describe what happens to the values in the sequence as n increases.<br \/>\nb. Describe the set of possible values for r. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe rule for a recursive sequence is as follows.<br \/>\nf(1) = 3, f(2) = 10<br \/>\nf(n) = 4 + 2f(n \u2212 1) \u2212f (n \u2212 2)<br \/>\na. Write the first five terms of the sequence.<br \/>\nb. Use finite differences to find a pattern. What type of relationship do the terms of the sequence show?<br \/>\nc. Write an explicit rule for the sequence.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45797\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-67.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 67\" width=\"553\" height=\"440\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-67.png 553w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-67-300x239.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 68.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says it is impossible to write a recursive rule for a sequence that is neither arithmetic nor geometric. Is your friend correct? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe first four triangular numbers T<sub>n<\/sub> and the first four square numbers S<sub>n<\/sub> are represented by the points in each diagram.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38711\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-18.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 18\" width=\"229\" height=\"199\" \/><br \/>\na. Write an explicit rule for each sequence.<br \/>\nb. Write a recursive rule for each sequence.<br \/>\nc. Write a rule for the square numbers in terms of the triangular numbers. Draw diagrams to explain why this rule is true.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45798\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-69.1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 69.1\" width=\"577\" height=\"581\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-69.1.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-69.1-298x300.png 298w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-69.1-150x150.png 150w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45799\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-69.2.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 69.2\" width=\"594\" height=\"253\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-69.2.png 594w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-69.2-300x128.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 70.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou are saving money for retirement. You plan to withdraw $30,000 at the beginning of each year for 20 years after you retire. Based on the type of investment you are making, you can expect to earn an annual return of 8% on your savings after you retire.<br \/>\na. Let a<sub>n<\/sub> be your balance n years after retiring. Write a recursive equation that shows how a<sub>n<\/sub> is related to a<sub>n-1<\/sub>.<br \/>\nb. Solve the equation from part (a) for a<sub>n-1<\/sub>. Find a<sub>0<\/sub>, the minimum amount of money you should have in your account when you retire. (Hint: Let a<sub>20<\/sub> = 0.)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/10\/fcd49520e4f1a8f6aef21c9a7b0bb72c\/cfe5e54dc5d7de0ba6a4a109199b3afb\/lateximg.png?tcb=1622051930\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 71.<br \/>\n\\(\\sqrt{x}\\) + 2 = 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45800\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-71.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 71\" width=\"474\" height=\"128\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-71.png 474w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-71-300x81.png 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>Question 72.<br \/>\n2\\(\\sqrt{52}\\) \u2212 5 = 15<br \/>\nAnswer:<br \/>\n2\\(\\sqrt{52}\\) \u2212 5 = 15<br \/>\n2\\(\\sqrt{52}\\) = 20<br \/>\n\\(\\sqrt{52}\\) = 20\/2<br \/>\n\\(\\sqrt{52}\\) = 10<br \/>\n52 \u2260 100<\/p>\n<p>Question 73.<br \/>\n\\(\\sqrt [ 3 ]{ x }\\) + 16 = 19<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45801\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-73.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 73\" width=\"510\" height=\"151\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-73.png 510w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-73-300x89.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 74.<br \/>\n2\\(\\sqrt [ 3 ]{ x }\\) \u2212 13 = \u22125<br \/>\nAnswer:<br \/>\n2\\(\\sqrt [ 3 ]{ x }\\) \u2212 13 = \u22125<br \/>\n2\\(\\sqrt [ 3 ]{ x }\\) = -5 + 13<br \/>\n2\\(\\sqrt [ 3 ]{ x }\\) = 8<br \/>\n\\(\\sqrt [ 3 ]{ x }\\) = 4<br \/>\nx = 64<\/p>\n<p>The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 4.<br \/>\nQuestion 75.<br \/>\nx = 2, y = 9<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45802\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-75.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 75\" width=\"394\" height=\"225\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-75.png 394w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-75-300x171.png 300w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><\/p>\n<p>Question 76.<br \/>\nx =\u22124, y = 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/04\/a53d93387062af7c11ad8fcd351780eb\/56db31f634cdac7b0ae3d67c52387fd6\/lateximg.png?tcb=1622051986\" \/><\/p>\n<p>Question 77.<br \/>\nx = 10, y = 32<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-45803\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-77.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 a 77\" width=\"402\" height=\"229\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-77.png 402w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-a-77-300x171.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<h3><a id=\"Sequences_and_Series_Performance_Task:_Integrated_Circuits_and_Moore_s_Law\"><\/a>Sequences and Series Performance Task: Integrated Circuits and Moore s Law<\/h3>\n<p><strong>8.4\u20138.5What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\npartial sum, p. 436<br \/>\nexplicit rule, p. 442<br \/>\nrecursive rule, p. 442<\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 8.4<br \/>\nPartial Sums of Infinite Geometric Series, p. 436<br \/>\nThe Sum of an Infinite Geometric Series, p. 437<\/p>\n<p>Section 8.5<br \/>\nEvaluating Recursive Rules, p. 442<br \/>\nRecursive Equations for Arithmetic and Geometric Sequences, p. 442<br \/>\nTranslating Between Recursive and Explicit Rules, p. 444<\/p>\n<p><strong>Mathematical Practices<\/strong><br \/>\nQuestion 1.<br \/>\nDescribe how labeling the axes in Exercises 3\u20136 on page 439 clarifies the relationship between the quantities in the problems.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nWhat logical progression of arguments can you use to determine whether the statement in Exercise 30 on page 440 is true?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nDescribe how the structure of the equation presented in Exercise 40 on page 448 allows you to determine the starting salary and the raise you receive each year.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nDoes the recursive rule in Exercise 61 on page 449 make sense when n= 5? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>Performance Task: Integrated Circuits and Moore s Law<\/strong><\/p>\n<p>In April of 1965, an engineer named Gordon Moore noticed how quickly the size of electronics was shrinking. He predicted how the number of transistors that could fit on a 1-inch diameter circuit would increase over time. In 1965, only 50 transistors fit on the circuit. A decade later, about 65,000 transistors could fit on the circuit. Moore\u2019s prediction was accurate and is now known as Moore\u2019s Law. What was his prediction? How many transistors will be able to fit on a 1-inch circuit when you graduate from high school?<br \/>\nTo explore the answers to this question and more, go to BigIdeasMath.com.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38712\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-19.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 8 Sequences and Series 8.5 19\" width=\"316\" height=\"337\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-19.png 316w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-8-Sequences-and-Series-8.5-19-281x300.png 281w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><\/p>\n<h3><a id=\"Sequences_and_Series_Chapter_Review\"><\/a>Sequences and Series Chapter Review<\/h3>\n<p><strong>8.1 Defining and Using Sequences and Series (pp. 409\u2013416)<\/strong><\/p>\n<p>Question 1.<br \/>\nDescribe the pattern shown in the figure. Then write a rule for the nth layer of the figure, where n = 1 represents the top layer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38713\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-cr-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series cr 1\" width=\"122\" height=\"88\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113685\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-1JPG.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-1JPG.jpg\" width=\"268\" height=\"230\" \/><\/p>\n<p><strong>Write the series using summation notation.<\/strong><br \/>\nQuestion 2.<br \/>\n7 + 10 + 13 +. . .+ 40<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/04\/cc993fe30be1e8c5d16664bd51d69eeb\/3228453a4019fad0c3d2ad88f6593e14\/lateximg.png?tcb=1622094164\" \/><\/p>\n<p>Question 3.<br \/>\n0 + 2 + 6 + 12 +. . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/04\/e517280dd9d44605017a39ace1c1a154\/ef096371aaf72d709ce587765348bdc2\/lateximg.png?tcb=1622094190\" \/><\/p>\n<p><strong>Find the sum<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\sum_{i=2}^{7}\\)(9 &#8211; i<sup>3<\/sup>)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/04\/192ff8b3c6de87ee5ac159ce0d895d1c\/8cb473517517476e9fec955f2391543b\/lateximg.png?tcb=1622094241\" \/><\/p>\n<p>Question 5.<br \/>\n\\(\\sum_{i=1}^{46}\\)i<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/04\/13c9754a3a897610345699c09349e14f\/2f106b281aa0aa93b54e87765f1853a8\/lateximg.png?tcb=1622094413\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\sum_{i=1}^{12}\\)i<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/04\/7171b828d9ffdf7d7a3645b31948ae26\/4ecf543996847763b1154609f66c5cbe\/lateximg.png?tcb=1622094288\" \/><\/p>\n<p>Question 7.<br \/>\n\\(\\sum_{i=1}^{5} \\frac{3+i}{2}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/04\/8d249bdf9c8fc02c2acb7894ff0a6f0d\/f13684f3e0ba248ff8bfbad6f8ba0955\/lateximg.png?tcb=1622094320\" \/><\/p>\n<p><strong>8.2 Analyzing Arithmetic Sequences and Series (pp. 417\u2013424)<\/strong><\/p>\n<p>Question 8.<br \/>\nTell whether the sequence 12, 4, \u22124, \u221212, \u221220, . . . is arithmetic. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/04\/20bf1d0a4d5d1dc1db7b4d8446caa487\/4fd91970e69a6fa07d7f7c0742b7e97f\/lateximg.png?tcb=1622094439\" \/><\/p>\n<p>Write a rule for the nth term of the arithmetic sequence. Then graph the first six terms of the sequence.<br \/>\nQuestion 9.<br \/>\n2, 8, 14, 20, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113693\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-9.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-9.jpg\" width=\"507\" height=\"713\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-9.jpg 507w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-9-213x300.jpg 213w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 10.<br \/>\na<sub>14<\/sub> = 42, d = 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-113695\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-10.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-10.jpg\" width=\"535\" height=\"660\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-10.jpg 607w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-10-243x300.jpg 243w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-113696\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-10a.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-10.jpg\" width=\"348\" height=\"279\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-10a.jpg 652w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-10a-300x241.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 11.<br \/>\na<sub>6<\/sub> = \u221212, a<sub>12<\/sub> = \u221236<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/04\/7a40cc34a6b512aa7f6c78a3b44a49d1\/1d3d69a2bff0e5071c19ff20ccfd0533\/lateximg.png?tcb=1622099961\" \/><\/p>\n<p>Question 12.<br \/>\nFind the sum \\(\\sum_{i=1}^{36}\\)(2 + 3i) .<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nYou take a job with a starting salary of $37,000. Your employer offers you an annual raise of $1500 for the next 6 years. Write a rule for your salary in the nth year. What are your total earnings in 6 years?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/04\/caa7610cd058727eaa6c5c655f593e2c\/15fc01c7a90780ec0cf46144aba331ed\/lateximg.png?tcb=1622099864\" \/><\/p>\n<p><strong>8.3 Analyzing Geometric Sequences and Series (pp. 425\u2013432)<\/strong><\/p>\n<p>Question 14.<br \/>\nTell whether the sequence 7, 14, 28, 56, 112, . . . is geometric. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113716\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-14.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-14.jpg\" width=\"234\" height=\"185\" \/><\/p>\n<p>Write a rule for the nth term of the geometric sequence. Then graph the first six terms of the sequence.<br \/>\nQuestion 15.<br \/>\n25, 10, 4, \\(\\frac{8}{5}\\) , . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113720\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-15.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-15.jpg\" width=\"478\" height=\"835\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-15.jpg 478w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-15-172x300.jpg 172w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>Question 16.<br \/>\na<sub>5<\/sub> = 162, r =\u22123<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113723\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-16.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-16.jpg\" width=\"603\" height=\"913\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-16.jpg 603w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-16-198x300.jpg 198w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>Question 17.<br \/>\na<sub>3<\/sub> = 16, a<sub>5<\/sub> = 256<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113725\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-17.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-17.jpg\" width=\"575\" height=\"891\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-17.jpg 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-17-194x300.jpg 194w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-113726\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-17a.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-17a.jpg\" width=\"515\" height=\"327\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-17a.jpg 642w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-17a-300x191.jpg 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Question 18.<br \/>\nFind the sum \\(\\sum_{i=1}^{9}\\)5(\u22122)<sup>i\u22121<\/sup> .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/a52846438f67a6ac9badf6f2c61a32b2\/de9e5ca83d58580e657dedc4595f9e6f\/lateximg.png?tcb=1622101422\" \/><\/p>\n<p><strong>8.4 Finding Sums of Infinite Geometric Series (pp. 435\u2013440)<\/strong><\/p>\n<p>Question 19.<br \/>\nConsider the infinite geometric series 1, \u2212\\(\\frac{1}{4}, \\frac{1}{16},-\\frac{1}{64}, \\frac{1}{256}, \\ldots\\) Find and graph the partial sums S<sub>n<\/sub> for n= 1, 2, 3, 4, and 5. Then describe what happens to S<sub>n<\/sub> as n increases.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-113730\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-19.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-19.jpg\" width=\"551\" height=\"823\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-19.jpg 601w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-19-201x300.jpg 201w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-113733\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-19a.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-19.jpg\" width=\"521\" height=\"553\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-19a.jpg 642w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-19a-283x300.jpg 283w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p>Question 20.<br \/>\nFind the sum of the infinite geometric series \u22122 + \\(\\frac{1}{2}-\\frac{1}{8}+\\frac{1}{32}+\\cdots\\), if it exists.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/f1419b4c872bc0cbe8ca67f7f2b36ff8\/071621b37ee888606139b546ded8c5d2\/lateximg.png?tcb=1622101820\" \/><\/p>\n<p>Question 21.<br \/>\nWrite the repeating decimal 0.1212 . . . as a fraction in simplest form.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/5cf3995bd0c3d0addc8428e9b5a88c1e\/865610c0d4a9f320a3f089b415ad0b23\/lateximg.png?tcb=1622101881\" \/><\/p>\n<p><strong>8.5 Using Recursive Rules with Sequences (pp. 441\u2013450)<\/strong><\/p>\n<p><strong>Write the first six terms of the sequence.<\/strong><br \/>\nQuestion 22.<br \/>\na<sub>1<\/sub> = 7, a<sub>n<\/sub> = a<sub>n-1<\/sub> + 11<br \/>\nAnswer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113738\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-22.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-review-Answer-22.jpg\" width=\"283\" height=\"260\" \/><\/p>\n<p>Question 23.<br \/>\na<sub>1<\/sub> = 6, a<sub>n<\/sub> = 4a<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\na<sub>1<\/sub> = 6<br \/>\na<sub>n<\/sub> = 4a<sub>n-1<\/sub><br \/>\na2 = 4a2-1<br \/>\na2 = 4a1<br \/>\na2 = 4(6) = 24.<br \/>\na3 = 4(24) = 96<br \/>\na4 = 4(96) = 384<br \/>\na5 = 4(384) =1,536<br \/>\na6 = 4( 1,536) = 6,144<\/p>\n<p>Question 24.<br \/>\nf(0) = 4, f(n) = f(n \u2212 1) + 2n<br \/>\nAnswer:<br \/>\nf(0) = 4 and f(n) = f(n-1) + 2n<br \/>\nIf n = 1.<br \/>\nf(1) = f(1-1) + 2(1)<br \/>\n= f(0) + 2 = 4 + 1 = 5<br \/>\nn = 2<br \/>\nf(2) = f(2-1) + 2(2) = 5 + 4<br \/>\nf(2) = 9.<br \/>\nn = 3<br \/>\nf(3) = f(3-1) + 2(3)<br \/>\nf(3) = f(2) + 6 = 9 + 6<br \/>\nf(3) = 15.<br \/>\nf(4) = f(4-1) + 2(4)<br \/>\nf(4) = f(3) + 8 = 15 + 8<br \/>\nf(4) = 23.<br \/>\nf(5) = f(5-1) + 2(5) = f(4) + 10<br \/>\n= 23 + 10<br \/>\nf(5) = 33.<br \/>\nf(6) = f(6-1) + 2(6) = f(5) + 12<br \/>\n= 33 + 12<br \/>\nf(6) = 45<\/p>\n<p><strong>Write a recursive rule for the sequence.<\/strong><br \/>\nQuestion 25.<br \/>\n9, 6, 4, \\(\\frac{8}{3}\\), \\(\\frac{16}{9}\\), . . .<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n2, 2, 4, 12, 48, . . .<br \/>\nAnswer:<br \/>\n2, 2, 4, 12, 48, . . .<br \/>\na1 = 2,<br \/>\na2 = 2 = 1 x 2 = 1 x a1.<br \/>\na3 = 4 = 2 x 2 = 2 x a2.<br \/>\na4 = 12 = 3 x 4 = 3 x a3.<br \/>\na5 = 48 = 4 x 12 = 4 x a4.<br \/>\nWe can conclude that<br \/>\nan = (n-1)an-1<br \/>\nThe recursive rule for the sequence is a1 = 2, an = (n-1) x an-1.<\/p>\n<p>Question 27.<br \/>\n7, 3, 4, \u22121, 5, . . .<br \/>\nAnswer:<br \/>\n7, 3, 4, \u22121, 5, . . .<br \/>\nHere a1 = 7, a2 = 3, a3 = 4, a5 = -1, a6 = 5.<br \/>\nThe recursive rule for the sequence is an = an-2 &#8211; an-1.<\/p>\n<p>Question 28.<br \/>\nWrite a recursive rule for a<sub>n<\/sub> = 105 (\\(\\frac{3}{5}\\))<sup>n\u22121<\/sup> .<br \/>\nAnswer:<br \/>\nan = 105(\\(\\frac{3}{5}\\))<sup>n\u22121<\/sup> .<br \/>\nWe know that,<br \/>\nan = a1 x r<sup>n\u22121<\/sup><br \/>\na1 = 105 and r = \\(\\frac{3}{5}\\).<br \/>\nan = r x a<sup>n\u22121<\/sup> .<br \/>\nan = \\(\\frac{3}{5}\\) a<sup>n\u22121<\/sup> .<br \/>\nSo, the recursive equation is an = \\(\\frac{3}{5}\\)a<sup>n\u22121<\/sup> .<\/p>\n<p>Write an explicit rule for the sequence.<br \/>\nQuestion 29.<br \/>\na<sub>1<\/sub> = \u22124, a<sub>n<\/sub> = a<sub>n-1<\/sub> + 26<br \/>\nAnswer:<br \/>\na1 = -4, an = an-1 + 26.<br \/>\nLet n = 2.<br \/>\na2 = a2-1 + 26 = a1 + 26 = -4 + 26 = 22.<br \/>\na3 = a3-1 + 26 = a2 + 26 = 22 + 26 = 48.<br \/>\na4 = a4-1 + 26 = a3 + 26 = 48 + 26 = 74.<br \/>\na5 = a5-1 + 26 = a4 + 26 = 74 + 26 = 100.<br \/>\na6 = a6-1 + 26 = a5 + 26 = 100 + 26 = 126.<\/p>\n<p>Question 30.<br \/>\na<sub>1<\/sub> = 8, a<sub>n<\/sub> = \u22125a<sub>n-1<\/sub><br \/>\nAnswer:<br \/>\na1 = 8, an = -5an-1.<br \/>\nLet n = 2.<br \/>\na2 = -5(a2-1) = -5a1 = -5(8) = 40.<br \/>\na3 = -5(a3-1) = -5a2 = -5(40) = -200.<br \/>\na4 = -5(a4-1) = -5a3 = -5(-200) = 1000.<br \/>\na5 = -5(a5-1) = -5a4 = -5(1000) = -5000.<br \/>\na6 = -5(a6-1) = -5a5 = -5(-5000) = 25,000.<\/p>\n<p>Question 31.<br \/>\na<sub>1<\/sub> = 26, a<sub>n<\/sub> = \\(\\frac{2}{5}\\)a<sub>n-1<\/sub>.<br \/>\nAnswer:<br \/>\na1 = 26, an = 2\/5 (an-1)<br \/>\nLet n = 2<br \/>\na2 = 2\/5 (a2-1) = 2\/5 (a1) = 2\/5 x 26 = 10.4<br \/>\na3 = 2\/5 (a3-1) = 2\/5 (a2) = 2\/5 x 10.4 = 4.16<br \/>\na4 = 2\/5 (a4-1) = 2\/5 (a3) = 2\/5 x 4.16 = 1.664<br \/>\na5 = 2\/5 (a5-1) = 2\/5 (a4) = 2\/5 x 1.664 = 0.6656<br \/>\na6 = 2\/5 (a6-1) = 2\/5 (a5) = 2\/5 x 0.6656 = 0.26624.<\/p>\n<p>Question 32.<br \/>\nA town\u2019s population increases at a rate of about 4% per year. In 2010, the town had a population of 11,120. Write a recursive rule for the population P<sub>n<\/sub> of the town in year n. Let n = 1 represent 2010.<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nThe numbers 1, 6, 15, 28, . . . are called hexagonal numbers because they represent the number of dots used to make hexagons, as shown. Write a recursive rule for the nth hexagonal number.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38714\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-cr-33.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series cr 33\" width=\"243\" height=\"82\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Sequences_and_Series_Chapter_Test\"><\/a>Sequences and Series Chapter Test<\/h3>\n<p><strong>Find the sum.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\sum_{i=1}^{24}\\)(6i\u2212 13)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/f55ccbd2fa3f64b5f48876933824eb75\/ec8f880b207c8d3c254b080c8b29a1f2\/lateximg.png?tcb=1622105101\" \/><\/p>\n<p>Question 2.<br \/>\n\\(\\sum_{n=1}^{16}\\)n<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/a557727525ced1a3231c922f66d48904\/c9a29b9e2dd1b74c1b18a21721bb8987\/lateximg.png?tcb=1622105070\" \/><\/p>\n<p>Question 3.<br \/>\n\\(\\sum_{k=1}^{\\infty}\\)2(0.8)<sup>k\u22121<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\\(\\sum_{i=1}^{6}\\)4(\u22123)<sup>i\u22121<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/2436d4fbbf3ba8a50dc7baaa25b5f0ac\/af1fa51cac1d4d539c3ecc1e1e862053\/lateximg.png?tcb=1622105030\" \/><\/p>\n<p>Determine whether the graph represents an arithmetic sequence, geometric sequence, or neither. Explain your reasoning. Then write a rule for the nth term.<br \/>\nQuestion 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38715\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-ct-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series ct 5\" width=\"120\" height=\"132\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/f223b52683652342739046f21136ad3b\/58580ccb4d19ff2799d550c777001b96\/lateximg.png?tcb=1622104969\" \/><\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38716\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-ct-6.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series ct 6\" width=\"119\" height=\"135\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/95ca5c88329c62a91c094a87bd64f6b8\/01a413a2cedbcc04c7211942325310bf\/lateximg.png?tcb=1622104942\" \/><\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38717\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-ct-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series ct 7\" width=\"159\" height=\"135\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113747\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-tes-Answer-7.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-tes-Answer-7.jpg\" width=\"546\" height=\"890\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-tes-Answer-7.jpg 546w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-tes-Answer-7-184x300.jpg 184w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p><strong>Write a recursive rule for the sequence. Then find a<sub>9<\/sub>.<\/strong><br \/>\nQuestion 8.<br \/>\na<sub>1<\/sub> = 32, r = \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/383fae196f9f734a0c6e06cf9e2920dd\/a91792d36576e0aabced664ea19fb4a2\/lateximg.png?tcb=1622105148\" \/><\/p>\n<p>Question 9.<br \/>\na<sub>n<\/sub> = 2 + 7n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/b550a39f85c46bf1710434993a05d998\/ea9d842838d02ece322eeb28eb49d827\/lateximg.png?tcb=1622105194\" \/><\/p>\n<p>Question 10.<br \/>\n2, 0, \u22123, \u22127, \u221212, . . .<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/728312cea131e5c36847a572e2bc6da6\/29f92ccc44485267e1bdd734b1ff0f8f\/lateximg.png?tcb=1622105221\" \/><\/p>\n<p>Question 11.<br \/>\nWrite a recursive rule for the sequence 5, \u221220, 80, \u2212320, 1280, . . .. Then write an explicit rule for the sequence using your recursive rule.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/21\/04\/06\/7cc4cf96237a6d148911ce9d790031c3\/00d500ec7a0da493d42a18e7c099fc08\/lateximg.png?tcb=1622105257\" \/><\/p>\n<p>Question 12.<br \/>\nThe numbers a, b, and c are the first three terms of an arithmetic sequence. Is b half of the sum of a and c? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/12\/59070cea21ef853dc684bf1d4ea8966b\/321f282c2301b1f1a9f27c0cfd6279f4\/lateximg.png?tcb=1622105294\" \/><\/p>\n<p>Question 13.<br \/>\nUse the pattern of checkerboard quilts shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38718\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-ct-8.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series ct 8\" width=\"454\" height=\"95\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-ct-8.png 454w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-ct-8-300x63.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><br \/>\na. What does n represent for each quilt? What does an represent?<br \/>\nb. Make a table that shows n and an for n= 1, 2, 3, 4, 5, 6, 7, and 8.<br \/>\nc. Use the rule a<sub>n<\/sub> = \\(\\frac{n^{2}}{2}+\\frac{1}{4}\\)[1 \u2212 (\u22121)<sup>n<\/sup>] to find an for n = 1, 2, 3, 4, 5, 6, 7, and 8.<br \/>\nCompare these values to those in your table in part (b). What can you conclude? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113750\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-tes-Answer-13.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-tes-Answer-13.jpg\" width=\"320\" height=\"380\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-tes-Answer-13.jpg 320w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-ideas-math-Algebra-2-Chapter-8-Sequences-and-series-Chapter-tes-Answer-13-253x300.jpg 253w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/p>\n<p>Question 14.<br \/>\nDuring a baseball season, a company pledges to donate $5000 to a charity plus $100 for each home run hit by the local team. Does this situation represent a sequence or a series? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/12\/00df13c4f2868a6089eff3652abbc929\/4ff8ad89a44dd33de5d33aa87423171b\/lateximg.png?tcb=1622105442\" \/><\/p>\n<p>Question 15.<br \/>\nThe length\u21131 of the first loop of a spring is 16 inches. The length\u21132 of the second loop is 0.9 times the length of the first loop. The length\u21133 of the third loop is 0.9 times the length of the second loop, and so on. Suppose the spring has infinitely many loops, would its length be finite or infinite? Explain. Find the length of the spring, if possible.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38719\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-8-Sequences-and-Series-ct-15.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series ct 15\" width=\"239\" height=\"143\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" src=\"https:\/\/d2nchlq0f2u6vy.cloudfront.net\/15\/09\/12\/12ea2810b19f956f9b73ecc4f7723ad0\/ba45d5d368fe7b0bd3e7e819af80491a\/lateximg.png?tcb=1622105464\" \/><\/p>\n<h3><a id=\"Sequences_and_Series_Cumulative_Assessment\"><\/a>Sequences and Series Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nThe frequencies (in hertz) of the notes on a piano form a geometric sequence. The frequencies of G (labeled 8) and A (labeled 10) are shown in the diagram. What is the approximate frequency of E at (labeled 4)?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38720\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series ca 1\" width=\"402\" height=\"150\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-1.png 402w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-1-300x112.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nYou take out a loan for $16,000 with an interest rate of 0.75% per month. At the end of each month, you make a payment of $300.<br \/>\na. Write a recursive rule for the balance an of the loan at the beginning of the nth month.<br \/>\nb. How much do you owe at the beginning of the 18th month?<br \/>\nc. How long will it take to pay off the loan?<br \/>\nd. If you pay $350 instead of $300 each month, how long will it take to pay off the loan? How much money will you save? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nThe table shows that the force F (in pounds) needed to loosen a certain bolt with a wrench depends on the length \u2113 (in inches) of the wrench\u2019s handle. Write an equation that relates \u2113 and F. Describe the relationship.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38721\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series ca 3\" width=\"258\" height=\"81\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nOrder the functions from the least average rate of change to the greatest average rate of change on the interval 1 \u2264 x \u2264 4. Justify your answers.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38722\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series ca 4\" width=\"423\" height=\"258\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-4.png 423w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-4-300x183.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nA running track is shaped like a rectangle with two semicircular ends, as shown. The track has 8 lanes that are each 1.22 meters wide. The lanes are numbered from 1 to 8 starting from the inside lane. The distance from the center of a semicircle to the inside of a lane is called the curve radius of that lane. The curve radius of lane 1 is 36.5 meters, as shown in the figure.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38723\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series ca 5\" width=\"336\" height=\"173\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-5.png 336w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-5-300x154.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><br \/>\na. Is the sequence formed by the curve radii arithmetic, geometric, or neither? Explain.<br \/>\nb. Write a rule for the sequence formed by the curve radii.<br \/>\nc. World records must be set on tracks that have a curve radius of at most 50 meters in the outside lane. Does the track shown meet the requirement? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nThe diagram shows the bounce heights of a basketball and a baseball dropped from a height of 10 feet. On each bounce, the basketball bounces to 36% of its previous height, and the baseball bounces to 30% of its previous height. About how much greater is the total distance traveled by the basketball than the total distance traveled by the baseball?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-38724\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8-Sequences-and-Series-ca-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series ca 6\" width=\"220\" height=\"210\" \/><br \/>\nA. 1.34 feet<br \/>\nB. 2.00 feet<br \/>\nC. 2.68 feet<br \/>\nD. 5.63 feet<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nClassify the solution(s) of each equation as real numbers, imaginary numbers, or pure imaginary numbers. Justify your answers.<br \/>\na. x + \\(\\sqrt{-16}\\) = 0<br \/>\nb. (11 &#8211; 2i) &#8211; (-3i + 6) = 8 + x<br \/>\nc. 3x<sup>2<\/sup> &#8211; 14 = -20<br \/>\nd. x<sup>2<\/sup> + 2x = -3<br \/>\ne. x<sup>2<\/sup> = 16<br \/>\nf. x<sup>2<\/sup> &#8211; 5x &#8211; 8 = 0<br \/>\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hey guys!!! Are you looking for the best guide to solve the Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series Questions? If our guess is correct, then you are on the right page. Here the students can get Big Ideas Math Algebra 2 Answers Ch 8 Sequences and Series with brief &#8230; <a title=\"Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series\" class=\"read-more\" href=\"https:\/\/ccssanswers.com\/big-ideas-math-algebra-2-answers-chapter-8\/\" aria-label=\"More on Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":49931,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-8.png","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/38537"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=38537"}],"version-history":[{"count":6,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/38537\/revisions"}],"predecessor-version":[{"id":162428,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/38537\/revisions\/162428"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media\/49931"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=38537"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=38537"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=38537"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}