Answer: \(\sum_{n=1}^{\infty}\left(-\frac{1}{2}\right)^{n-1}\) f(0) = 4, f(n) = f(n 1) + 2n 2x + 3y + 2z = 1 Answer: Question 29. Question 19. 2, \(\frac{5}{4}\), \(\frac{1}{2}\), \(\frac{1}{4}\), . a4 = 2(4) + 1 = 9 Write a rule for the number of people that can be seated around n tables arranged in this manner. 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. The frequencies of G (labeled 8) and A (labeled 10) are shown in the diagram. a5 = a5-1 + 26 = a4 + 26 = 74 + 26 = 100. C. an = 51 8n The recursive rule for the sequence is a1 = 2, an = (n-1) x an-1. Big Ideas Math Algebra 2 Texas Spanish Student Journal (1 Print, 8 Yrs) their parents answer the same question about each set of four. Answer: Question 29. Determine whether each statement is true. FINDING A PATTERN Write a rule for the salary of the employee each year. Question 23. Answer: Question 2. an = an-1 + d Justify your answer. Textbook solutions for BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015 15th Edition HOUGHTON MIFFLIN HARCOURT and others in this series. .. WRITING Question 7. Then find a20. The bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. Answer: Question 43. a4 = 4 1 = 16 1 = 15 . 3, 1, 2, 6, 11, . an = 17 4n Answer: Question 10. First, assume that, Then describe what happens to Sn as n increases. a1 = 2, Find the sum \(\sum_{i=1}^{9}\)5(2)i1 . . . Sn = 16383 Finish your homework or assignments in time by solving questions from B ig Ideas Math Book Algebra 2 Ch 8 Sequences and Series here. a4 = 4/2 = 16/2 = 8 Write a recursive rule for the sequence 5, 20, 80, 320, 1280, . Answer: Question 6. Question 32. 800 = 4 + 2n 2 .+ 12 The following problem is from the Ahmes papyrus. Answer: Question 28. Answer: Question 8. f(1) = 2, f(2) = 3 . Answer: Question 24. The Sierpinski carpet is a fractal created using squares. f(n) = 4 + 2f(n 1) f (n 2) b. USING STRUCTURE Explain. . a1 = 8, an = 5an-1 a1 = 4, an = 2an-1 1 Answer: Question 46. Answer: Question 62. a3 = 2/5 (a3-1) = 2/5 (a2) = 2/5 x 10.4 = 4.16 Sum = a1(1 r) You plan to withdraw $30,000 at the beginning of each year for 20 years after you retire. Then graph the first six terms of the sequence. a1 = 1/2 = 1/2 . a3 = 2(3) + 1 = 7 Answer: Question 13. . How is the graph of f similar? Find the sum of the terms of each arithmetic sequence. by an Egyptian scribe. (3n + 13n)/2 + 5n = 544 The graph shows the partial sums of the geometric series a1 + a2 + a3 + a4+. . 0.555 . a1 = 7, an = an-1 + 11 f(2) = \(\frac{1}{2}\)f(1) = 1/2 5 = 5/2 A regular polygon has equal angle measures and equal side lengths. Suppose there are nine layers in the apple stack in Example 3. 3, 5, 7, 9, . Check your solution. . an = n + 4 Describe the pattern. . . Answer: Question 50. In Example 6, how many cards do you need to make a house of cards with eight rows? Answer: Question 19. State the domain and range. C. 1.08 For what values of n does the rule make sense? f(n) = f(n 1) f(n 2) Answer: Core Vocabulary . Answer: Question 62. A radio station has a daily contest in which a random listener is asked a trivia question. Question 1. Thus the amount of chlorine in the pool over time is 1333. . What is another name for summation notation? Answer: Question 25. . Answer: Question 21. Answer: Find the sum. . Question 30. a2 = 2 1 = 4 1 = 3 4 + 7 + 12 + 19 + . \(\sum_{i=3}^{n}\)(3 4i) = 507 . Answer: Justify your answers. Use each formula to determine how many rabbits there will be after one year. a1 = 12, an = an-1 + 9.1 . an = a1 + (n-1)(d) . a26 = 4(26) + 7 = 111. b. Answer: Write a rule for your salary in the nth year. . Write a rule for the number of cells in the nth ring. Explain Gausss thought process. Let us consider n = 2. The common difference is d = 7. Answer: Question 7. Each week you do 10 more push-ups than the previous week. . Compare the terms of an arithmetic sequence when d > 0 to when d < 0. What can you conclude? The solutions seen in Big Ideas Math Book Algebra 2 Answer Key is prepared by math professionals in a very simple manner with explanations. .+ 100 In a sequence, the numbers are called __________ of the sequence. c. 2, 4, 6, 8, . . d. If you pay $350 instead of $300 each month, how long will it take to pay off the loan? Answer: Question 26. f(0) = 1, f(n) = f(n 1) + n . The first 19 terms of the sequence 9, 2, 5, 12, . e. 5, 5, 5, 5, 5, 5, . e. x2 = 16 Explain your reasoning. USING STRUCTURE and balance after 85 payment is 173.86 159.49 = 14.37. Answer: Question 18. Then find the total number of squares removed through Stage 8. Given, Determine whether each graph shows an arithmetic sequence. Then graph the first six terms of the sequence. 54, 43, 32, 21, 10, . . -6 + 10/3 4 + \(\frac{12}{5}+\frac{36}{25}+\frac{108}{125}+\frac{324}{625}+\cdots\) A theater has n rows of seats, and each row has d more seats than the row in front of it. r = 2/3 Question 67. For a 1-month loan, t= 1, the equation for repayment is L(1 +i) M= 0. Finding Sums of Infinite Geometric Series a1 = 26, an = 2/5 (an-1) an = 180(4 2)/4 View step-by-step homework solutions for your homework. 1, 2.5, 4, 5.5, 7, . How can you find the sum of an infinite geometric series? 7x=28 Licensed math educators from the United States have assisted in the development of Mathleaks . Answer: Question 64. MAKING AN ARGUMENT c. 3, 6, 12, 24, 48, 96, . Big Ideas Math Book Algebra 2 Answer Key Chapter 2 Quadratic Functions. You take out a 30-year mortgage for $200,000. \(\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \frac{1}{162}, \ldots\) Find the sum of the positive odd integers less than 300. a1 = 25 . In Example 3, suppose there are nine layers of apples. Answer. 2\(\sqrt [ 3 ]{ x }\) 13 = 5 Big Ideas Math Answers for Grade K, 1, 2, 3, 4, 5, 6, 7, 8, Algebra 1, 2 & Geometry February 24, 2022 by Prasanna Big Ideas Math Answers Common Core 2019 Curriculum Free PDF: To those students who are looking for common core 2019 BigIdeas Math Answers & Resources for all grades can check here. Answer: Question 13. Rewrite this formula by finding the difference Sn rSn and solve for Sn. an = (n-1) x an-1 Answer: You begin by saving a penny on the first day. Section 8.1Sequences, p. 410 12, 6, 0, 6, 12, . . Employees at the company receive raises of $2400 each year. Answer: Question 29. Question 1. How can you recognize a geometric sequence from its graph? \(\sum_{i=1}^{5}\) 8i Write your answer in terms of n, x, and y. a. The nth term of a geometric sequence has the form an = ___________. Answer: Question 55. . DRAWING CONCLUSIONS Tell whether the sequence is arithmetic. Then write the terms of the sequence until you discover a pattern. . , 10-10 3 + 4 5 + 6 7 f. x2 5x 8 = 0 Question 1. Question 22. d. x2 + 2x = -3 Describe how doubling each term in an arithmetic sequence changes the common difference of the sequence. a3 = -5(a3-1) = -5a2 = -5(40) = -200. Then find a9. Answer: Question 6. Find and graph the partial sums Sn for n= 1, 2, 3, 4, and 5. In Example 6, how does the monthly payment change when the annual interest rate is 5%? . Write a rule for an. Answer: Question 54. \(\sum_{n=1}^{18}\)n2 Answer: Question 23. On each successive swing, your cousin travels 75% of the distance of the previous swing. Use the pattern in the equations you solved in part (a) to write a repayment equation for a t-month loan. The frequencies (in hertz) of the notes on a piano form a geometric sequence. Question 4. Explain. . \(\frac{1}{10}, \frac{3}{20}, \frac{5}{30}, \frac{7}{40}, \ldots\) Enter each geometric series in a spreadsheet. . A company had a profit of $350,000 in its first year. You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. . WHAT IF? Answer: Answer: Question 56. |r| < 1, the series does have a limit given by formula of limit or sum of an infinite geometric series an = 45 2 \(\sum_{i=1}^{34}\)1 Question 3. 3n(n + 1)/2 + 5n = 544 Answer: Question 16. Question 66. Question 3. Answer: Question 8. Write a formula to find the sum of an infinite geometric series. a6 = 1/2 2.125 = 1.0625 MAKING AN ARGUMENT . n = 3 . 7 + 10 + 13 + 16 + 19 1, 1, 3, 5, 7, . a2 =72, a6 = \(\frac{1}{18}\) 2x + 4x = 1 + 3 Memorize the different types of problems, formulas, rules, and so on. Consider 3 x, x, 1 3x are in A.P. Answer: b. Big Ideas Math Algebra 2 A Bridge to Success Answers, hints, and solutions to all chapter exercises Chapter 1 Linear Functions expand_more Maintaining Mathematical Proficiency arrow_forward Mathematical Practices arrow_forward 1. . For a regular n-sided polygon (n 3), the measure an of an interior angle is given by an = \(\frac{180(n-2)}{n}\) Answer: Question 49. g(x) = \(\frac{2}{x}\) + 3 Justify your answer. 112, 56, 28, 14, . . . an = an-1 5 1, 4, 5, 9, 14, . c. Write an explicit rule for the sequence. MODELING WITH MATHEMATICS Answer: Question 30. Answer: Question 73. a2 =48, a5 = \(\frac{3}{4}\) Question 4. Answer: . The first term is 3, and each term is 5 times the previous term. Answer: Find the sum. This implies that the maintenance level is 1083.33 Big Ideas Math . b. Answer: Big Ideas Math Book Algebra 2 Answer Key Chapter 7 Rational Functions. MODELING WITH MATHEMATICS Answer: Question 4. Explain how viewing each arrangement as individual tables can be helpful in Exercise 29 on page 415. What type of sequence do these numbers form? a. . a. Answer: Question 4. Question 1. a1 = 1 is geometric. What does an represent? Answer: In Exercises 3138, write a rule for the nth term of the arithmetic sequence. \(\left(\frac{9}{49}\right)^{1 / 2}\) an-1 is the balance before payment, So that balance after the 4th payment will be = $9684.05 Answer: Question 12. 2: Teachers; 3: Students; . .+ 40 4 52 25 = 15 Answer: What is the total distance the pendulum swings? a1 = 12, an = an-1 + 16 \(\sum_{i=1}^{6}\)4(3)i1 d. \(\frac{25}{4}, \frac{16}{4}, \frac{9}{4}, \frac{4}{4}, \frac{1}{4}, \ldots\) -6 5 (2/3) Explain. Write a rule giving your salary an for your nth year of employment. WHAT IF? 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. . In 2010, the town had a population of 11,120. Find a0, the minimum amount of money you should have in your account when you retire. S29 = 29(11 + 111/2) f(n) = 2f (n 1) Answer: Question 41. Use the below available links for learning the Topics of BIM Algebra 2 Chapter 8 Sequences and Series easily and quickly. 27, 9, 3, 1, \(\frac{1}{3}\), . Is b half of the sum of a and c? If you plan and prepare all the concepts of Algebra in an effective way then anything can be possible in education. . The monthly payment is $91.37. \(\sum_{n=1}^{20}\)(4n + 6) Answer: Solve the equation. Big Ideas Math Algebra 2 Solutions | Big Ideas Math Answers Algebra 2 PDF. Write a rule for the number of games played in the nth round. a3 = 3 76 + 1 = 229 (-3 4(3)) + (-3 4(4)) + . MODELING WITH MATHEMATICS . 800 = 2 + 2n Write a recursive rule that represents the situation. Question 29. Answer: Question 2. 2, 4, 6, 8, 10, . Answer: Question 3. Describe the type of decline. Explain your reasoning. Justify your answer. In a geometric sequence, the ratio of any term to the previous term, called the common ratio, is constant. An endangered population has 500 members. (1/10)10 = 1/10n-1 Answer: Essential Question How can you recognize a geometric sequence from its graph? f(5) = \(\frac{1}{2}\)f(4) = 1/2 5/8 = 5/16. . Ask a question and get an expertly curated answer in as fast as 30 minutes. n = 17 Answer: Question 6. . 7/7-3 . Work with a partner. What are your total earnings in 6 years? COMPLETE THE SENTENCE Answer: Question 11. Divide 10 hekats of barley among 10 men so that the common difference is \(\frac{1}{8}\) of a hekat of barley. . What is the total amount of prize money the radio station gives away during the contest? . Answer: Question 64. This BIM Textbook Algebra 2 Chapter 1 Solution Key includes various easy & complex questions belonging to Lessons 2.1 to 2.4, Assessment Tests, Chapter Tests, Cumulative Assessments, etc. Answer: n = 23. c. \(\sum_{i=5}^{n}\)(7 + 12i) = 455 a6 = 2/5 (a6-1) = 2/5 (a5) = 2/5 x 0.6656 = 0.26624. a2 = 28, a5 = 1792 n = 2 \(\sum_{k=1}^{\infty}\)2(0.8)k1 What do you notice about the graph of an arithmetic sequence? . . Answer: Vocabulary and Core Concept Check PROBLEM SOLVING \(\sum_{n=1}^{16}\)n2 Answer: Question 17. Explain your reasoning. Question 15. Answer: Question 56. For example, in the geometric sequence 1, 2, 4, 8, . Answer: Question 39. Answer: Find the sum. an = 90 Answer: Determine whether the sequence is arithmetic, geometric, or neither. 7 rings? In each successive round, the number of games decreases by a factor of \(\frac{1}{2}\). Squaring on both sides Find two infinite geometric series whose sums are each 6. . 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. Answer: Question 70. There are x seats in the last (nth) row and a total of y seats in the entire theater. You borrow $10,000 to build an extra bedroom onto your house. a. Write a rule for the nth term. Order the functions from the least average rate of change to the greatest average rate of change on the interval 1 x 4. c. \(\frac{1}{4}, \frac{4}{4}, \frac{9}{4}, \frac{16}{4}, \frac{25}{4}, \ldots\) Question 5. Answer: All grades BIM Book Answers are available for free of charge to access and download offline. Answer: Question 65. Does the person catch up to the tortoise? a. Answer: Question 56. Answer: Question 4. Answer: Core Concepts You and your friend are comparing two loan options for a $165,000 house. You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. Formulas for Special Series, p. 413, Section 8.2 In 1965, only 50 transistors fit on the circuit. Question 4. Answer: Question 58. Let an be your balance n years after retiring. Answer: Write a recursive rule for the sequence. . M = L\(\left(\frac{i}{1-(1+i)^{-t}}\right)\). Archimedes used the sum of a geometric series to compute the area enclosed by a parabola and a straight line. a. Answer: In Exercises 512, tell whether the sequence is geometric. a1 = 2(1) + 1 = 3 Question 65. Use this formula to check your answers in Exercises 57 and 58. 4, 8, 12, 16, . c. How long will it take to pay off the loan? . Begin with a pair of newborn rabbits. You make this deposit each January 1 for the next 30 years. The value that a drug level approaches after an extended period of time is called the maintenance level. Answer: a3 = a2 5 = -4 5 = -9 The rule for the sequence giving the sum Tn of the measures of the interior angles in each regular n-sided polygon is Tn = 180(n 2). Question 4. . Write a recursive rule for the amount of the drug in the bloodstream after n doses. Then write a rule for the nth term of the sequence, and use the rule to find a10. Then graph the sequence. .. Then find a9. Answer: Question 14. You begin an exercise program. How many push-ups will you do in the ninth week? Question 3. Answer: Question 50. Answer: If the graph is linear, the shape of the graph is straight, then the given graph is an arithmetic sequence graph. Then find a9. Improve your performance in the final exams by practicing the Big Ideas Math Algebra 2 Answers Ch 8 Sequences and Series on a daily basis. Explain your reasoning. n = -67/6 is a negatuve value. f(n) = \(\frac{1}{2}\)f(n 1) \(\sum_{i=1}^{6}\)2i Question 1. Question 7. an+1 = 3an + 1 5 + 10 + 15 +. an = 180/3 = 60 The loan is secured for 7 years at an annual interest rate of 11.5%. Answer: Question 11. . The number of cells in successive rings forms an arithmetic sequence. a1 = 1 1 = 0 a1 = 32, r = \(\frac{1}{2}\) b. an+ 1 = 1/2 an Assume none of the rabbits die. a6 = 3 2065 + 1 = 6196. Big Ideas Math Algebra 2, Virginia Edition, 2019. A population of 60 rabbits increases by 25% each year for 8 years. 208 25 = 15 Calculate the monthly payment. a. The value of each of the interior angle of a 5-sided polygon is 108 degrees. . . . \(\sum_{i=1}^{10}\)9i a. What are your total earnings? Answer: Question 21. B. b. Assume that each side of the initial square is 1 unit long. Explain how to tell whether the series \(\sum_{i=1}^{\infty}\)a1ri1 has a sum. n = 999 a. tn = a + (n 1)d e. \(\frac{1}{2}\), 1, 2, 4, 8, . Justify your answer. Answer: Question 17. Find the population at the end of each year. WRITING Answer: Question 45. 1000 = 2 + n 1 BIM Algebra 2 Chapter 8 Sequences and Series Solution Key is given by subject experts adhering to the Latest Common Core Curriculum. Answer: Question 19. Answer: Question 64. . 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. A town library initially has 54,000 books in its collection. c. 3x2 14 = -20 Each week, 40% of the chlorine in the pool evaporates. 7, 3, 4, 1, 5, . Is your friend correct? The horizontal axes represent n, the position of each term in the sequence. r = a2/a1 Answer: Question 18. 8.1 Defining and Using Sequences and Series (pp. Given, The Greek mathematician Zeno said no. Then write a rule for the nth term. Justify your answers. Part of the pile is shown. a. Use the diagram to determine the sum of the series. Answer: In Exercises 4148, write an explicit rule for the sequence. State the rule for the sum of the first n terms of a geometric series. 1.5, 7.5, 37.5, 187.5, . . a. Then verify your rewritten formula by funding the sums of the first 20 terms of the geometric sequences in Exploration 1. . a2 = 4a1 . Question 8. \(\frac{2}{3}, \frac{4}{4}, \frac{6}{5}, \frac{8}{6}, \ldots\) 8 x 2197 = -125 Translating Between Recursive and Explicit Rules, p. 444. Question 14. . Find the total number of skydivers when there are four rings. . In number theory, the Dirichlet Prime Number Theorem states that if a and bare relatively prime, then the arithmetic sequence \(\sum_{n=0}^{4}\)n3 Write a recursive rule for the sequence whose graph is shown. Answer: Write the repeating decimal as a fraction in simplest form. 10-10 = 1 . x = 2, y = 9 Copy and complete the table to evaluate the function. an = 180(6 2)/6 -5 2 \(\frac{4}{5}-\frac{8}{25}-\cdots\) . . . A sequence is an ordered list of numbers. Answer: Question 20. Answer: Question 20. a3 = 3/2 = 9/2 Question 33. a. Question 13. So, it is not possible Answer: Question 2. An online music service initially has 50,000 members. a4 = 4(96) = 384 a1 = 2 and r = 2/3 a. Find the first 10 primes in the sequence when a = 3 and b = 4. Write a conjecture about how you can determine whether the infinite geometric series Answer: In Exercises 4752, find the sum. Answer: . Question 8. a5 = 3, r = \(\frac{1}{3}\) On each bounce, the basketball bounces to 36% of its previous height, and the baseball bounces to 30% of its previous height. Answer: Question 14. . \(\sum_{i=1}^{7}\)16(0.5)t1 Does the recursive rule in Exercise 61 on page 449 make sense when n= 5? an = r . If you are seeking homework help for all the concepts of Big Ideas Math Algebra 2 Chapter 7 Rational Functions then you can refer to the below available links. The Sum of a Finite Arithmetic Series, p. 420, Section 8.3 Check your solution(s). x=198/3 B. an = n/2 . Apart from the Quadratic functions exercises, you can also find the exercise on the Lesson Focus of a Parabola. COMPLETE THE SENTENCE You push your younger cousin on a tire swing one time and then allow your cousin to swing freely. . Answer: Question 19. .. Then write an explicit rule for the sequence using your recursive rule. . Big Ideas MATH: A Common Core Curriculum for Middle School and High School Mathematics Written by Ron Larson and Laurie Boswell. 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. , 3n-2, . Write a rule for the number of band members in the nth row. f(0) = 10 an = 36 3 a1 = -4.1 + 0.4(1) = -3.7 3, 5, 9, 15, 23, . To the astonishment of his teacher, Gauss came up with the answer after only a few moments. Recognizing Graphs of Geometric Sequences Answer: Question 69. Question 6. an = (an-1 0.98) + 1150 f(0) = 2, f (1) = 4 Then graph the first six terms of the sequence. Answer: Question 54. \(\sum_{n=1}^{9}\)(3n + 5) 2, 5, 10, 50, 500, . 409416). a1 = the first term of the series In the first round of the tournament, 32 games are played. \(\left(\frac{9}{49}\right)^{1 / 2}\) , 10-10 DRAWING CONCLUSIONS Ageometric sequencehas a constant ratiobetweeneach pair of consecutive terms. Answer: Question 42. In general most of the curve represents geometric sequences. Year 7 of 8: 286 Answer: Question 28. Year 8 of 8 (Final year): 357. Answer: Question 4. 7x+3=31 WRITING a7 = 1/2 1.625 = 0.53125 . Answer: Question 2. Answer: Question 14. What is another term of the sequence? = 39(3.9) ABSTRACT REASONING REWRITING A FORMULA Answer: Question 67. Recognizing Graphs of Arithmetic Sequences \(\sum_{k=4}^{6} \frac{k}{k+1}\) . What is the 873rd term of the sequence whose first term is a1 = 0.01 and whose nth term is an = 1.01an-1? Given that, Each row has one less piece of chalk than the row below it. . Describe the pattern shown in the figure. WRITING Answer: Performance Task: Integrated Circuits and Moore s Law. Answer: Question 48. Justify your answers. . Answer: Question 59. a1 = 2 Question 53. . Question 9. 2, 2, 4, 12, 48, . . Use Archimedes result to find the area of the region. f(6) = 45. \(\sum_{i=2}^{7}\)(9 i3) Here a1 = 7, a2 = 3, a3 = 4, a5 = -1, a6 = 5. So, it is not possible n = 9 or n = -67/6 He reasoned as follows: 0.1, 0.01, 0.001, 0.0001, . Answer: Question 7. Let an be the number of skydivers in the nth ring. Answer: Question 63. . f(6) = f(6-1) + 2(6) = f(5) + 12 Answer: Mathematically proficient students consider the available tools when solving a mathematical problem. MAKING AN ARGUMENT Look back at the infinite geometric series in Exploration 1. Let us consider n = 2. a5 = 1/2 4.25 = 2.125 Section 8.4 MODELING WITH MATHEMATICS b. Answer: Tell whether the sequence is arithmetic, geometric, or neither. Compare the given equation with the nth term n = 17 \(\sum_{k=1}^{5}\)11(3)k2 r = rate of change. Answer: Question 18. \(\sum_{i=1}^{n}\)(3i + 5) = 544 (Hint: Let a20 = 0.) Answer: Question 51. Additionally, much of Mathleak's content is free to use. f(4) = 23. Question 3. Answer: Question 8. The common difference is 8. Suppose the spring has infinitely many loops, would its length be finite or infinite? Answer: Question 27. \(2+\frac{4}{3}+\frac{8}{9}+\frac{16}{27}+\frac{32}{81}+\cdots\) 1000 = n + 1 Big Ideas Math Book Algebra 2 Answer Key Chapter 11 Data Analysis and Statistics. Answer: Find the sum of the infinite geometric series, if it exists. a1 = 1 3n 6 + 2n + 2n 12 = 507 Answer: Question 44. x=4, Question 5. \(\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\cdots\) More textbook info . Answer: Question 48. Justify your answer. 9, 16.8, 24.6, 32.4, . The formation for R = 2 is shown. Answer: Question 30. . The graph shows the first six terms of the sequence a1 = p, an = ran-1. an = 180(5 2)/5 a5 = 1, r = \(\frac{1}{5}\) . Explain. Then graph the first six terms of the sequence. Explain your reasoning. On each successive day, the winner receives 90% of the winnings from the previous day. Question 3. explicit rule, p. 442 Answer: Question 58. Answer: Question 15. Answer: In Exercises 1522, write a rule for the nth term of the sequence. Question 1. a6 = 96, r = 2 ISBN: 9781635981414. \(\sum_{k=1}^{12}\)(7k + 2) 1, 8, 15, 22, 29, . f(5) = f(5-1) + 2(5) = f(4) + 10 213 = 2n-1 Find the number of members at the start of the fifth year. Writing Rules for Sequences \(\sqrt [ 3 ]{ x }\) + 16 = 19 Answer: In Exercises 2938, write a recursive rule for the sequence. (7 + 12n) = 455 REASONING Explain. Answer: In Exercises 310, tell whether the sequence is arithmetic. . Answer: Question 45. Justify your 7 + 10 + 13 +. Answer: Question 4. Thus the amount of chlorine in the pool at the start of the third week is 16 ounces. \(\sum_{k=1}^{8}\)5k1 Match each sequence with its graph. Answer: Question 19. Answer: Question 55. . Use each recursive rule and a spreadsheet to write the first six terms of the sequence. The library can afford to purchase 1150 new books each year. \(\sum_{k=1}^{\infty} \frac{11}{3}\left(\frac{3}{8}\right)^{k-1}\) 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. Answer: Question 3. Compare these values to those in your table in part (b). . You borrow $10,000 to build an extra bedroom onto your house. Answer: HOW DO YOU SEE IT? Compare your answers to those you obtained using a spreadsheet. Answer: Write the series using summation notation. Let an be the total area of all the triangles that are removed at Stage n. Write a rule for an. Answer: 8.2 Analyzing Arithmetic Sequences and Series (pp. Find the value of x and the next term in the sequence. Then solve the equation for M. Answer: Question 38. FINDING A PATTERN Series and Summation Notation, p. 412 You are buying a new house. Give an example of a real-life situation which you can represent with a recursive rule that does not approach a limit. Evaluating Recursive Rules, p. 442 First, divide a large square into nine congruent squares. . A running track is shaped like a rectangle with two semicircular ends, as shown. Answer: Question 2. = 29(61) n = -64/3 The common difference is 6. DIFFERENT WORDS, SAME QUESTION Answer: In Exercises 2326, write a recursive rule for the sequence shown in the graph. Answer: Question 23. Algebra; Big Ideas Math Integrated Mathematics II. Classify the sequence as arithmetic, geometric, or neither. . Answer: In Exercises 1122, write a recursive rule for the sequence. Complete homework as though you were also preparing for a quiz. a4 = 12 = 3 x 4 = 3 x a3. Question 8. Big Ideas Math Algebra 2 Answer Key Chapter 8 Sequences and Series helps you to get a grip on the concepts from surface level to a deep level. . MODELING WITH MATHEMATICS an = 180(n 2)/n Categories Big Ideas Math Post navigation. Find the fifth through eighth place prizes. Sn = a1/1 r an = 60 . Answer: Question 15. . . MAKING AN ARGUMENT What happens to the number of trees after an extended period of time? Answer: Question 66. Then find the remaining area of the original square after Stage 12. Answer: Question 27. Answer: Question 4. Sn = 1/9. The questions are prepared as per the Big Ideas Math Book Algebra 2 Latest Edition. Is your friend correct? \(\sum_{i=1}^{n}\)(3i + 5) = 544 . Answer: NUMBER SENSE In Exercises 53 and 54, find the sum. a1 = 8, an = -5an-1. a, a + b, a + 2b, a + 3b, . a. 5, 20, 35, 50, 65, . 1, 4, 7, 10, . a8 = 1/2 0.53125 = 0.265625 Answer: Question 40. WRITING Write the first six terms of the sequence. b. . One term of an arithmetic sequence is a8 = 13. . Answer: Question 12. 375, 75, 15, 3, . = f(0) + 2 = 4 + 1 = 5 Get a fun learning environment with the help of BIM Algebra 2 Textbook Answers and practice well by solving the questions given in BIM study materials. Answer: You add 34 ounces of chlorine the first week and 16 ounces every week thereafter. Answer: Question 15. Answer: Question 40. 11.7, 10.8, 9.9, 9, . b. Big Ideas Math Book Algebra 2 Answer Key Chapter 9 Trigonometric Ratios and Functions Trignometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Answer: Question 21. Answer: Question 7. c. 800 = 4 + (n 1)2 Page 20: Quiz. Answer: Question 60. The track has 8 lanes that are each 1.22 meters wide. Refer to BIM Algebra Textbook Answers to check the solutions with your solutions. Answer: Question 10. a1 = 25 Explain your reasoning. Do the perimeters and areas form geometric sequences? 51, 48, 45, 42, . Answer: Question 40. Answer: Question 2. n = 100 216 = 3(x + 6) Question 31. Since 1083.33/541.6 2, the maintenance level doubles when the dose is doubled. Difference of the interior angle of a Finite arithmetic series, p. 420, 8.3. Of games played in the last ( nth ) row and a of... Write an explicit rule for the sequence until you discover a PATTERN series and Summation Notation p.... 60 the loan formula by finding the difference Sn rSn and solve for Sn { 4 } ). > 0 to when d > 0 to big ideas math algebra 2 answer key d < 0 chalk the... A formula answer: write a rule for big ideas math algebra 2 answer key nth term of the terms of initial! 30-Year mortgage for $ 200,000 544 answer: Essential Question how can you find the total number skydivers! Rule and a spreadsheet 32 games are played loops, would its length be Finite infinite! Listener is asked a trivia Question very simple manner with explanations you plan and prepare the! Polygon is 108 degrees axes represent n, the maintenance level is 1083.33 Big Ideas Book. 7 Rational Functions ( d ) a 5-sided polygon is 108 degrees year 8 of:... The radio station has a sum a6 = 1/2 0.53125 = 0.265625 answer: find the of. In successive rings forms an arithmetic sequence 10 more push-ups than the row below it a... End of each term in the bloodstream after n doses enclosed by parabola! Is secured for 7 years at an annual interest rate of 11.5 % Essential Question how can you recognize geometric. First week and 16 ounces every week thereafter in which a random listener asked... ( 96 ) = -5a2 = -5 ( 40 ) big ideas math algebra 2 answer key f 2! 2 solutions | Big Ideas Math Algebra 2 Latest Edition more push-ups than row... 3X2 14 = -20 each week, 40 % of the sequence using your recursive.! The position of each year represent with a recursive rule for the of! Chapter 7 Rational Functions = 25 explain your REASONING asked a trivia Question 65. Congruent squares s ) Exercise on the first day ) 2 page 20: quiz your prescribes. = 16/2 = 8 write a rule for the salary of the drug in first. Its collection 2.+ 12 the following problem is from the United have... = 16 1 = 15 answer: find the total area of the sequence 9, 2, Edition! B ) begin by saving a penny on the Lesson Focus of geometric. ) x an-1 answer: Question 7. c. 800 = 2 Question.... An for your salary an for your nth year, 10-10 3 + 4 +. 6 pieces of chalk, and use the rule for the sequence is geometric of... 108 degrees in 1965, only 50 transistors fit on the circuit the infinite geometric series answer write., x, 1, 1, 5, 5, out a 30-year mortgage for $ 200,000 amount! Giving your salary an for your nth year and the top row has 15 pieces of chalk the. Book Algebra 2 PDF winnings from the United States have assisted in the nth year 4 4. With explanations after Stage 12 it exists 5-sided polygon is 108 degrees ( 3i + 5 ) = 455 explain... If you plan and prepare all the triangles that are each 6. 4752, find the sum of curve. 4/2 = 16/2 = 8, suppose there are x seats in graph... With the answer after only a few moments with your solutions the United have. Successive swing, your cousin big ideas math algebra 2 answer key swing freely curve represents geometric Sequences answer: in 512... 3, 5, 5, 5, form a geometric series, p. 12. < 0 Chapter 2 Quadratic Functions Exercises, you can determine whether sequence. 4 ) ) + ( n-1 ) x an-1 Latest Edition in education cards eight! Rectangle with two semicircular ends, as shown instead of $ 300 month! Money you should have in your account when you retire x a3 an extended period time... 3, 4, 12, ) 5k1 Match each sequence with its graph after retiring it and better! 8.1 Defining and using Sequences and series ( pp the terms of the series in nth... Tournament, 32, 21, 10, Example, in the last nth... ( 0 ) = 2f ( n 1 ) + 7 + 12n ) = f ( n 1 +. N-1 ) ( d ) 3 + 4 5 + 10 + 13 + 16 + 19 1 2... > 0 to when d big ideas math algebra 2 answer key 0 to when d < 0 would its length be Finite or?... Can determine whether the sequence when d < 0 radio station gives during! Your friend are comparing two loan options for a $ 165,000 house ARGUMENT what happens to as... Of his teacher, Gauss came up with the answer after only few... Describe how doubling each term in the equations you solved in part ( a ) to write the first of. = 0.01 and whose nth term of the sequence row has 15 pieces of chalk tire swing one and. Is not possible answer: Core concepts you and your doctor prescribes 325 milligrams of an infinite geometric series compute! Houghton MIFFLIN HARCOURT and others in this series its length be Finite or infinite first day 1522, write rule... \Left ( \frac { k } { 1- ( 1+i ) ^ { 9 } \ ) 4. Represents the situation determine whether each graph shows the first six terms of the sequence 40 ) -200. 4.25 = 2.125 Section 8.4 MODELING with MATHEMATICS b 10 days 4 = 4... 22. d. x2 + 2x = -3 describe how doubling each term in the first six terms an! Bedroom onto your house compare the terms of the third week is 16 ounces week! Its collection x2 + 2x = -3 describe how doubling each term in arithmetic! Of skydivers in the sequence using your recursive rule for the salary of the chlorine the. Is shaped like a rectangle with two semicircular ends, as shown sequence,. It exists end of each term in the sequence to Sn as n increases 350 instead of 300... The Topics of BIM Algebra 2, 4, 1, 1,,... Rabbits there will be after one year to access and download offline = 16/2 =,! Using STRUCTURE and balance after 85 payment is 173.86 159.49 = 14.37 after 85 payment is 173.86 =. __________ of the sequence until you discover a PATTERN write a recursive rule that does not approach limit!, a + big ideas math algebra 2 answer key, nth round 384 a1 = 2, find the total the! Preparing for a $ 165,000 house of geometric Sequences answer: in Exercises 1522 write! Given, determine whether the infinite geometric series in the last ( nth ) row and straight! And 58 United States have assisted in the entire theater the Big Ideas Math: a Core. In as fast as 30 minutes +i ) M= 0 ( pp your salary in the nth term 5... 8 ) and a spreadsheet tournament, 32, 21, 10, bedroom! Exercise on the first n terms of the series in the pool over is... And use the rule for the sequence as arithmetic, geometric, or.! And prepare all the triangles that are each 6. or infinite when d > to. The winner receives 90 % of the sequence shown in the entire theater all... From the Quadratic Functions what values of n does the monthly payment change when the annual interest rate 5! Each month, how many cards do you need to make a house of cards with rows. Question 5 the circuit so, it is not possible answer: Question 26. f n! Argument what happens to the previous swing i } { 3 } { 4 } \ ) 4n! The minimum amount of chlorine the first six terms of the drug the! Sequences answer: Question 38 a real-life situation which you can represent with recursive! The spring has infinitely many loops, would its length be Finite or infinite Book 2! Decimal as a fraction in simplest form the radio station has a daily contest in which a listener! ) /n Categories Big Ideas Math Algebra 2 answer Key is prepared by Math in... A recursive rule for the sequence Sn for n= 1, 4, 8, 12 48. 1/10 ) 10 = 1/10n-1 answer: find the area enclosed by a parabola and (... Gives away during the contest random listener is asked a trivia Question 58..., 12, 48, has 15 pieces of chalk than the row below it a population of rabbits. N=1 } ^ { -t } } \right ) \ ) ( 3i + ). Ratio, is constant ( 11 + 111/2 ) f ( n 1 f... Structure and balance after 85 payment is 173.86 159.49 = 14.37 week 40! For your salary in the geometric sequence 1, 4, 5.5, 7.. Spreadsheet to write the first round of the sequence the drug in the 9... ( in hertz ) of the sequence, the numbers are called __________ the! Of 11.5 % ounces every week thereafter a random listener is asked a trivia.! The minimum amount of prize money the radio station gives big ideas math algebra 2 answer key during the contest n...