Justify your answer. Each year, the company loses 20% of its current members and gains 5000 new members. . Answer: Question 48. What are your total earnings? f(4) = f(4-1) + 2(4) Year 8 of 8 (Final year): 357. 1 + 0.1 + 0.01 + 0.001 + 0.0001 +. Answer: Question 8. \(\sum_{i=1}^{7}\)16(0.5)t1 Answer: Question 65. 5, 10, 15, 20, . 2, 8, 14, 20, . a1 = 2 and r = 2/3 Answer: Question 68. Find the balance after the fifth payment. Answer: Question 31. \(\sum_{i=1}^{35}\)1 . 2. Assume that each side of the initial square is 1 unit long. an = an-1 5 Question 10. . Answer: Question 64. a5 = 1/2 4.25 = 2.125 .. Then find a15. Answer: Question 17. Question 29. Question 3. MAKING AN ARGUMENT an = (an-1)2 + 1 . a. Use the drop-down menu below to select your program. Which rule gives the total number of squares in the nth figure of the pattern shown? About how much greater is the total distance traveled by the basketball than the total distance traveled by the baseball? . Answer: Question 4. Question 47. \(\sum_{i=1}^{9}\)6(7)i1 Question 15. Answer: Write the series using summation notation. Question 11. Write the first six terms of the sequence. n = 100 Parent Functions and Transformations p. 3-10 2. Classify the solution(s) of each equation as real numbers, imaginary numbers, or pure imaginary numbers. Explain your reasoning. A. an = n 1 a1 = 32, r = \(\frac{1}{2}\) The length1 of the first loop of a spring is 16 inches. Question 1. The graph shows the first six terms of the sequence a1 = p, an = ran-1. 3n + 13n 1088 = 0 Answer: Question 27. Explain your reasoning. What do you notice about the graph of an arithmetic sequence? CRITICAL THINKING In Quadrature of the Parabola, he proved that the area of the region is \(\frac{4}{3}\) the area of the inscribed triangle. . Answer: Tell whether the sequence is arithmetic, geometric, or neither. f(0) = 4 and f(n) = f(n-1) + 2n Then verify your formula by checking the sums you obtained in Exploration 1. -4(n)(n + 1)/2 n = -1127 2, 0, 3, 7, 12, . a. . In a sequence, the numbers are called __________ of the sequence. . . Answer: Question 72. . . b. a1 = 6, an = 4an-1 2, 5, 8, 11, 14, . Answer: Solve the system. \(\sum_{n=0}^{4}\)n3 a21 = 25, d = \(\frac{3}{2}\) The common difference is 8. Justify your answer. an = 0.4 an-1 + 325 Thus, make use of our BIM Book Algebra 2 Solution Key Chapter 2 . Access the user-friendly solutions . In Exercises 514, write the first six terms of the sequence. . b. Compare the terms of an arithmetic sequence when d > 0 to when d < 0. f(n) = f(n 1) f(n 2) Answer: For a display at a sports store, you are stacking soccer balls in a pyramid whose base is an equilateral triangle with five layers. Your 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. Answer: Question 6. The constant difference between consecutive terms of an arithmetic sequence is called the _______________. You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. Answer: Question 14. With the help of BIM Algebra 2 Answer Key students can score good grades in any of their exams and can make you achieve what you are . Answer: Question 1. Then find a7. Given that, . Then graph the first six terms of the sequence. Answer: Question 49. Find the sum of the positive odd integers less than 300. \(\sum_{n=1}^{\infty} 3\left(\frac{5}{4}\right)^{n-1}\) . . Answer: Question 43. .+ 100 \(\sum_{n=1}^{\infty}\left(-\frac{1}{2}\right)^{n-1}\) Tell whether the function represents exponential growth or exponential decay. 3, 6, 9, 12, 15, 18, . Question 67. \(\frac{7}{7^{1 / 3}}\) Explain your reasoning. . Two terms of a geometric sequence are a6 = 50 and a9 = 6250. a5 = 41, a10 = 96 Answer: Question 61. If not, provide a counterexample. Mathleaks grants you instant access to expert solutions and answers in Big Ideas Learning's publications for Pre-Algebra, Algebra 1, Geometry, and Algebra 2. Answer: Question 16. Question 67. Repeat these steps for each smaller square, as shown below. . Answer: Question 11. Answer: ERROR ANALYSIS In Exercises 15 and 16, describe and correct the error in finding the sum of the infinite geometric series. Students can know the difference between trigonometric functions and trigonometric ratios from here. Write a rule for the sequence. . a. 0.3, 1.5, 7.5, 37.5, 187.5, . 2, \(\frac{5}{4}\), \(\frac{1}{2}\), \(\frac{1}{4}\), . an = r x an1 . 3. 7x+3=31 Answer. DRAWING CONCLUSIONS In 1965, only 50 transistors fit on the circuit. . Find the sum of the terms of each geometric sequence. In 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. Describe the pattern. The loan is secured for 7 years at an annual interest rate of 11.5%. Answer: Question 14. Write a rule for the number of people that can be seated around n tables arranged in this manner. n = -49/2 . Let an be the total area of all the triangles that are removed at Stage n. Write a rule for an. How can you define a sequence recursively? THOUGHT PROVOKING . Given, . Answer: Question 23. Question 9. Answer: Vocabulary and Core Concept Check an = 180(5 2)/5 Answer: Question 29. You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. Work with a partner. BIM Algebra 2 Chapter 8 Sequences and Series Solution Key is given by subject experts adhering to the Latest Common Core Curriculum. a3 = 16 a. a6 = 1/2 2.125 = 1.0625 Writing a Formula Justify your answer. Answer: Question 47. MAKING AN ARGUMENT 27, 9, 3, 1, \(\frac{1}{3}\), . Question 21. You take out a 30-year mortgage for $200,000. Describe the pattern shown in the figure. When n = 3 A recursive _________ tells how the nth term of a sequence is related to one or more preceding terms. Answer: Essential Question 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 an is related to one or more preceding terms. r = 4/3/2 Each ratio is 2/3, so the sequence is geometric Each week, 40% of the chlorine in the pool evaporates. 3x 2z = 8 Series and Summation Notation, p. 412 n = -49/2 is a negatuve value. Answer: Sequences and Series Maintaining Mathematical Proficiency Page 407, Sequences and Series Mathematical Practices Page 408, Lesson 8.1 Defining and Using Sequences and Series Page(409-416), Defining and Using Sequences and Series 8.1 Exercises Page(414-416), Lesson 8.2 Analyzing Arithmetic Sequences and Series Page(417-424), Analyzing Arithmetic Sequences and Series 8.2 Exercises Page(422-424), Lesson 8.3 Analyzing Geometric Sequences and Series Page(425-432), Analyzing Geometric Sequences and Series 8.3 Exercises Page(430-432), Sequences and Series Study Skills: Keeping Your Mind Focused Page 433, Sequences and Series 8.1 8.3 Quiz Page 434, Lesson 8.4 Finding Sums of Infinite Geometric Series Page(435-440), Finding Sums of Infinite Geometric Series 8.4 Exercises Page(439-440), Lesson 8.5 Using Recursive Rules with Sequences Page(441-450), Using Recursive Rules with Sequences 8.5 Exercises Page(447-450), Sequences and Series Performance Task: Integrated Circuits and Moore s Law Page 451, Sequences and Series Chapter Review Page(452-454), Sequences and Series Chapter Test Page 455, Sequences and Series Cumulative Assessment Page(456-457), Big Ideas Math Answers Grade 7 Accelerated, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 2 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 1 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 7 Module 2 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 7 Module 3 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 3 Module 2 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 3 Module 1 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 2 Answer Key. a1 = 4, an = an-1 + 26 . By this, you can finish your homework problems in time. . 86, 79, 72, 65, . Answer: Essential Question How can you write a rule for the nth term of a sequence? a0 = 162, an = 0.5an-1 How many seats are in the front row of the theater? Among them, bigideasmathanswer.com is a reliable and trusted site that offers Chapterwise Algebra 2 Big Ideas Math Book Answer Key for free of cost. NUMBER SENSE In Exercises 53 and 54, find the sum of the arithmetic sequence. f(0) = 4, f(n) = f(n 1) + 2n Question 1. a3 = -5(a3-1) = -5a2 = -5(40) = -200. D. an = 2n + 1 . 7x + 3 = 31 a. tn = arn-1 \(\sum_{i=1}^{n}\)1 = n b. Work with a partner. . Write a rule for the number of soccer balls in each layer. .What is the value of \(\sum_{n=1}^{\infty}\)an ? a4 = 4(4) = 16 Answer: Write a recursive rule for the sequence. Question 5. Sn = 16383 Write the first six terms of the sequence. Question 1. . Answer: Question 12. The lanes are numbered from 1 to 8 starting from the inside lane. Answer: WRITING EQUATIONS In Exercises 4146, write a rule for the sequence with the given terms. a. . Explain. \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots\) Then evaluate the expression. a. Answer: Question 63. \(\sum_{i=1}^{n}\)i2 = \(\frac{n(n+1)(2 n+1)}{6}\) Answer: Question 14. Answer: Question 9. a2 = 30, r = \(\frac{1}{2}\) Answer: Question 13. USING STRUCTURE MODELING WITH MATHEMATICS b. Then find the sum of the series. More textbook info . . Answer: Question 12. Find the sum of the infinite geometric series 2 + \(\frac{1}{2}-\frac{1}{8}+\frac{1}{32}+\cdots\), if it exists. 7n 28 + 6n + 6n 120 = 455 Answer: 8.2 Analyzing Arithmetic Sequences and Series (pp. Answer: Question 51. Answer: In Exercises 3138, write the series using summation notation. Tell whether the sequence 7, 14, 28, 56, 112, . = f(0) + 2 = 4 + 1 = 5 . \(\sum_{i=1}^{6}\)2i What is a rule for the nth term of the sequence? . .. Answer: Write the repeating decimal as a fraction in simplest form. DRAWING CONCLUSIONS The nth term of a geometric sequence has the form an = ___________. \(\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \frac{1}{162}, \ldots\) Answer: Question 19. Answer: Question 3. How many apples are in the stack? 2x + 4x = 1 + 3 Answer: Answer: Question 4. Write an explicit rule and a recursive rule for the sequence in part (a). Answer: Question 21. . Answer: Question 20. The Sum of a Finite Geometric Series, p. 428. (Hint: Let a20 = 0.) . Question 49. . a1 = 3, an = an-1 7 You have saved $82 to buy a bicycle. a26 = 4(26) + 7 = 111. WHAT IF? a5 = 3 688 + 1 = 2065 Question 31. c. Write an explicit rule for the number of cans in row n. Question 15. . . ABSTRACT REASONING d. If you pay $350 instead of $300 each month, how long will it take to pay off the loan? Answer: Question 50. Consider 3 x, x, 1 3x are in A.P. Then graph the sequence. Answer: Question 60. Answer: Question 17. Recursive Equations for Arithmetic and Geometric Sequences, p. 442 b. Then graph the sequence and classify it as arithmetic, geometric, or neither. S39 = 39(-3.7 + 11.5/2) 0.1, 0.01, 0.001, 0.0001, . Then graph the sequence. C. 1010 . . 2n(n + 1) + n = 1127 1, 4, 5, 9, 14, . Answer: Question 60. , 10-10 . Answer: Question 14. Answer: Question 56. When an infinite geometric series has a finite sum, what happens to r n as n increases? a1 = 26, an = \(\frac{2}{5}\)an-1. Answer: Question 17. . an = 180(4 2)/4 Answer: Question 15. Looking at the race as Zeno did, the distances and the times it takes the person to run those distances both form infinite geometric series. \(\sum_{i=1}^{26}\)(4i + 7) Question 1. 301 = 4 + 3n 3 Given that the sequence is 7, 3, 4, -1, 5. In each successive round, the number of games decreases by a factor of \(\frac{1}{2}\). Answer: (-3 4(3)) + (-3 4(4)) + . Show chapters. The first term is 7 and each term is 5 more than the previous term. Given, . Answer: Question 2. Answer: Find the sum of the infinite geometric series, if it exists. Answer: Begin with a pair of newborn rabbits. Then graph the first six terms of the sequence. The annual interest rate of the loan is 4%. y + z = 2 . Answer: Question 49. . . \(\sum_{n=1}^{5}\)(n2 1) b. . CRITICAL THINKING In a sequence, the numbers are called the terms of the sequence. 1, 1, 3, 5, 7, . f(3) = f(3-1) + 2(3) Big Ideas Math . 301 = 3n + 1 Answer: Determine whether the graph represents an arithmetic sequence, geometric sequence, or neither. . Answer: PROBLEM SOLVING Your friend claims the total amount repaid over the loan will be less for Loan 2. 3 + \(\frac{5}{2}+\frac{25}{12}+\frac{125}{72}+\cdots\) Answer: Question 25. MODELING WITH MATHEMATICS Order the functions from the least average rate of change to the greatest average rate of change on the interval 1 x 4. .. f. x2 5x 8 = 0 3x=198 Let us consider n = 2. All the solutions shown in BIM Algebra 2 Answers materials are prepared by math experts in simple methods. a. 4, 6, 9, \(\frac{27}{2}\), . . a1 = 1 THOUGHT PROVOKING Answer: \(2+\frac{4}{3}+\frac{8}{9}+\frac{16}{27}+\frac{32}{81}+\cdots\) . MATHEMATICAL CONNECTIONS Then find a9. Describe how doubling each term in an arithmetic sequence changes the common difference of the sequence. Answer: In Exercises 2326, write a recursive rule for the sequence shown in the graph. . .Terms of a sequence 0.1, 0.01, 0.001, 0.0001, . What can you conclude? c. \(\frac{1}{4}, \frac{4}{4}, \frac{9}{4}, \frac{16}{4}, \frac{25}{4}, \ldots\) 9, 16.8, 24.6, 32.4, . Answer: a2 = 64, r = \(\frac{1}{4}\) 2\(\sqrt [ 3 ]{ x }\) 13 = 5 Describe the type of decline. Answer: Question 45. \(\sum_{i=1}^{31}\)(3 4i ) 5 + 11 + 17 + 23 + 29 CRITICAL THINKING Answer: n = -35/2 is a negatuve value. 2n + 5n 525 = 0 Question 71. Answer: Question 15. \(\sqrt{x}\) + 2 = 7 Question 1. a4 = 4 1 = 16 1 = 15 Work with a partner. an = 10^-10 S29 = 29(11 + 111/2) an= \(\frac{1}{2}\left(\frac{1}{4}\right)^{n-1}\) Answer: Each week you do 10 more push-ups than the previous week. b. Answer: Question 68. A company had a profit of $350,000 in its first year. What happens to the number of books in the library over time? Use a spreadsheet to help you answer the question. The value of a car is given by the recursive rule a1 = 25,600, an = 0.86an-1, where n is the number of years since the car was new. Moores prediction was accurate and is now known as Moores Law. recursive rule, p. 442, Core Concepts Which graph(s) represents an arithmetic sequence? Answer: Question 5. Question 1. 1.2, 4.2, 9.2, 16.2, . \(\frac{1}{6}, \frac{1}{2}, \frac{5}{6}, \frac{7}{6}, \frac{3}{2}, \ldots\) \(\sum_{i=2}^{7}\)(9 i3) . 3, 1, 2, 6, 11, . \(\sum_{k=3}^{6}\)(5k 2) b. Anarithmetic sequencehas a constantdifference between each consecutive pair of terms. REWRITING A FORMULA 3n(n + 1)/2 + 5n = 544 a1 = 34 On the first day, the station gives $500 to the first listener who answers correctly. You want to save $500 for a school trip. D. 5.63 feet Describe the pattern, write the next term, and write a rule for the nth term of the sequence. an = 3/5 x an1 . You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. x + y + 4z =1 We have included Questions . Assume none of the rabbits die. Write a recursive rule for the number an of members at the start of the nth year. a11 = 50, d = 7 an-1 is the balance before payment, So that balance after the 4th payment will be = $9684.05 Answer: Question 12. . Answer: Question 2. Find the amount of the last payment. 3.1, 3.8, 4.5, 5.2, . a3 = 4, r = 2 How much money do you have in your account immediately after you make your last deposit? What are your total earnings in 6 years? Question 15. Write a recursive rule for the amount of chlorine in the pool at the start of the nth week. + (-3 4n) = -507 2.00 feet 2, \(\frac{3}{2}\), \(\frac{9}{8}\), \(\frac{27}{32}\), . Answer: Question 51. The first 19 terms of the sequence 9, 2, 5, 12, . . Answer: Question 4. 11, 22, 33, 44, 55, . Question 31. b. Then graph the first six terms of the sequence. Question 75. In Example 3, suppose there are nine layers of apples. 2, 14, 98, 686, 4802, . A tree farm initially has 9000 trees. . Sn = a(rn 1) 1/r 1 .+ 100 a12 = 38, a19 = 73 REWRITING A FORMULA . Answer: Question 35. Write a rule for the salary of the employee each year. Mathleaks offers learning-focused solutions and answers to commonly used textbooks for Algebra 2, 10th and 11th grade. How much money will you save? . Answer: Question 14. b. Take a pat the above links & download the respective grade of common core 2019 Big Ideas Math Book Answers Pdf to prepare . Answer: Question 9. Answer: Question 8. Answer: Rectangular tables are placed together along their short edges, as shown in the diagram. a4 = 2/5 (a4-1) = 2/5 (a3) = 2/5 x 4.16 = 1.664 216=3x+18 Work with a partner. Sequences and Series Big Ideas Math Algebra 2 Chapter 8 Answer Key encourages students and teachers to learn math in a simple and fun learning way. Page 20: Quiz. Answer: Question 4. . a1 = 4, an = 2an-1 1 51, 48, 45, 42, . Write a recursive rule for the nth hexagonal number. a2 = 3 25 + 1 = 76 . An online music service initially has 50,000 members. Find the length of the spring, if possible. Explain. (7 + 12(5)) + (7 + 12(6)) + . You borrow $10,000 to build an extra bedroom onto your house. How can you use tools to find the sum of the arithmetic series in Exercises 53 and 54 on page 423? when n = 6 Then, referring to this Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions is the best option. What is the total distance the pendulum swings? In April of 1965, an engineer named Gordon Moore noticed how quickly the size of electronics was shrinking. . Answer: Question 15. Use the sequence mode and the dot mode of a graphing calculator to graph the sequence. . x=4, Question 5. Answer: Answer: Question 8. . Answer: Question 36. Answer: Question 74. Use each recursive rule and a spreadsheet to write the first six terms of the sequence. Find the fifth through eighth place prizes. Question 3. . . The frequencies (in hertz) of the notes on a piano form a geometric sequence. Answer: Vocabulary and Core Concept Check You push your younger cousin on a tire swing one time and then allow your cousin to swing freely. a1 = -4.1 + 0.4(1) = -3.7 x 2z = 1 . Answer: Question 16. Answer: ERROR ANALYSIS In Exercises 31 and 32, describe and correct the error in writing a rule for the nth term of the geometric sequence for which a2 = 48 and r = 6. Let 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). 7x=28 Write a conjecture about how you can determine whether the infinite geometric series , 28, 56, 112, the baseball n as n increases the sequence an annual rate... 6 ) ) + 2 = 4 ( 4 ) ) + ( -3 4 3... N tables arranged in this manner 10,000 to build an extra bedroom onto your house Exercises 3138 write! Of an arithmetic sequence BIM Algebra 2 Answers materials are prepared by experts...: ERROR ANALYSIS in Exercises 15 and 16, describe and correct ERROR... Core Concept Check an = 0.4 an-1 + 325 Thus, make use our... In each layer in April of 1965, only 50 transistors fit on the circuit square is unit! 8, 11, piano form a geometric sequence row of the initial square is 1 long. Total number of books in the graph represents an arithmetic sequence /4 answer: 27... 11, 22, 33, 44, 55,, 187.5, moores prediction accurate... 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