f(2) = f(2-1) + 2(2) = 5 + 4 Answer: Question 33. Answer: Vocabulary and Core Concept Check b. Answer: an = 180(4 2)/4 1, \(\frac{1}{3}\), \(\frac{1}{3}\), 1, . \(\sum_{i=1}^{12}\)i2 Substitute r in the above equation. = f(0) + 2 = 4 + 1 = 5 2\(\sqrt{52}\) 5 = 15 The first 9 terms of the geometric sequence 14, 42, 126, 378, . Since then, the companys profit has decreased by 12% per year. Find the sum of each infinite geometric series, if it exists. Find step-by-step solutions and answers to Big Ideas Math Integrated Mathematics II - 9781680330687, as well as thousands of textbooks so you can move forward with confidence. b. Rule for an Arithmetic Sequence, p. 418 a2 = 3a1 + 1 . . 1, 4, 7, 10, . A. an = n 1 Explicit: fn = \(\frac{1}{\sqrt{5}}\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\frac{1}{\sqrt{5}}\left(\frac{1-\sqrt{5}}{2}\right)^{n}\), n 1 CRITICAL THINKING . Explain Gausss thought process. Then write a formula for the sum Sn of the first n terms of an arithmetic sequence. . 9, 6, 4, \(\frac{8}{3}\), \(\frac{16}{9}\), . Do the same for a1 = 25. Tell whether the sequence is geometric. a1 = 1/2 = 1/2 \(\sum_{i=1}^{9}\)6(7)i1 THOUGHT PROVOKING a1 = 12, an = an-1 + 16 The Sierpinski carpet is a fractal created using squares. Answer: Question 29. Question 5. Question 1. f(n) = \(\frac{n}{2n-1}\) MODELING WITH MATHEMATICS Answer: Question 13. 3.1, 3.8, 4.5, 5.2, . y= 2ex Using the table, show that both series have finite sums. 0.1, 0.01, 0.001, 0.0001, . \(\sum_{i=1}^{10}\)9i b. 800 = 4 + 2n 2 n = 15. Answer: Question 19. a6 = 96, r = 2 c. Put the value of n = 12 in the divided formula to get the sum of the interior angle measures in a regular dodecagon. . a4 = -5(a4-1) = -5a3 = -5(-200) = 1000. (9/49) = 3/7. Answer: Question 4. Question 3. Question 27. Answer: In Exercises 310, write the first six terms of the sequence. Answer: Question 6. In 2010, the town had a population of 11,120. You accept a job as an environmental engineer that pays a salary of $45,000 in the first year. Answer: Question 8. a3 = a2 5 = -4 5 = -9 c. Use the rule an = \(\frac{n^{2}}{2}+\frac{1}{4}\)[1 (1)n] to find an for n = 1, 2, 3, 4, 5, 6, 7, and 8. Calculate the monthly payment. Find the perimeter and area of each iteration. On each bounce, the basketball bounces to 36% of its previous height, and the baseball bounces to 30% of its previous height. Find the population at the end of each decade. The numbers 1, 6, 15, 28, . Our resource for Big Ideas Math: Algebra 2 Student Journal includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. a1 = 1 a3 = -5(a3-1) = -5a2 = -5(40) = -200. . \(\sum_{n=1}^{9}\)(3n + 5) . n = -64/3 f(1) = 3, f(2) = 10 The top eight runners finishing a race receive cash prizes. f(n) = 4 + 2f(n 1) f (n 2) The first 19 terms of the sequence 9, 2, 5, 12, . Question 59. You are buying a new house. 3 x + 3(2x 3) x = 259. Find the amount of the last payment. Answer. Translating Between Recursive and Explicit Rules, p. 444. When n = 3 a5 = 4(384) =1,536 an = a1 x rn1 .. a2 = 3 25 + 1 = 76 In Lesson 8.3, you learned that the sum of the first n terms of a geometric series with first term a1 and common ratio r 1 is . MAKING AN ARGUMENT Answer: Question 13. Question 1. a1 = 2, USING STRUCTURE Answer: Vocabulary and Core Concept Check a4 = -8/3 . nth term of a sequence Then write the area as the sum of an infinite geometric series. an = 180(n 2)/n MODELING WITH MATHEMATICS Write a recursive rule for the sequence and find its first eight terms. You and your friend are comparing two loan options for a $165,000 house. An endangered population has 500 members. Answer: 3n + 13n 1088 = 0 1000 = n + 1 . Answer: Question 14. To explore the answers to this question and more, go to BigIdeasMath.com. Then graph the first six terms of the sequence. \(\frac{2}{3}, \frac{4}{4}, \frac{6}{5}, \frac{8}{6}, \ldots\) Explain. This implies that the maintenance level is 1083.33 0, 1, 3, 7, 15, . 1, 8, 15, 22, 29, . * Ask an Expert *Response times may vary by subject and . Justify your answer. How can you define a sequence recursively? Our subject experts created this BIM algebra 2 ch 5 solution key as per the Common core edition BIM Algebra 2 Textbooks. Question 1. .. Question 27. Given that, f(3) = \(\frac{1}{2}\)f(2) = 1/2 5/2 = 5/4 Question 63. a4 = 4 1 = 16 1 = 15 A town library initially has 54,000 books in its collection. 1, 7, 13, 19, . Question 1. Answer: , 301 Big Ideas Math Book Algebra 2 Answer Key Chapter 2 Quadratic Functions. What happens to the population of fish over time? . . x=198/3 0 + 2 + 6 + 12 +. Answer: Question 24. Find the total number of skydivers when there are four rings. 19, 13, 7, 1, 5, . \(\sum_{i=1}^{12}\)6(2)i1 . . Let us consider n = 2 . e. x2 = 16 -18 + 10/3 The length3 of the third loop is 0.9 times the length of the second loop, and so on. What can you conclude? 112, 56, 28, 14, . Answer: Essential Question How can you recognize a geometric sequence from its graph? a18 = 59, a21 = 71 S = 6 Answer: Question 56. The bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. a. The solutions seen in Big Ideas Math Book Algebra 2 Answer Key is prepared by math professionals in a very simple manner with explanations. \(\sum_{i=2}^{8} \frac{2}{i}\) More textbook info . . MAKING AN ARGUMENT Let an be the total area of all the triangles that are removed at Stage n. Write a rule for an. a. You can find solutions for practice, exercises, chapter tests, chapter reviews, and cumulative assessments. \(\frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \ldots\) r = 4/3/2 f(0) = 10 Find the total number of games played in the regional soccer tournament. Answer: Write the repeating decimal as a fraction in simplest form. . Answer: Question 13. 15, 9, 3, 3, 9, . 1.5, 7.5, 37.5, 187.5, . c. You work 10 years for the company. . 7x + 3 = 31 Is the sequence formed by the curve radii arithmetic, geometric, or neither? \(\sum_{i=1}^{33}\)(6 2i ) an-1 is the balance before payment, So that balance after the 4th payment will be = $9684.05 Answer: Question 48. What is another name for summation notation? Work with a partner. First, assume that, Work with a partner. Question 67. a1 = 16, an = an-1 + 7 2n(n + 1) + n = 1127 Write a recursive rule that is different from those in Explorations 13. Match each sequence with its graph. Answer: How much money will you save? Answer: Question 21. A teacher of German mathematician Carl Friedrich Gauss (17771855) asked him to find the sum of all the whole numbers from 1 through 100. What logical progression of arguments can you use to determine whether the statement in Exercise 30 on page 440 is true? Write the first six terms of the sequence. . Answer: Question 19. Explain your reasoning. e. \(\frac{1}{2}\), 1, 2, 4, 8, . Given that, The inner square and all rectangles have a width of 1 foot. an = \(\frac{1}{4}\)(5)n-1 In the first round of the tournament, 32 games are played. Question 1. To the astonishment of his teacher, Gauss came up with the answer after only a few moments. Sign up. Compare sequences and series. If the graph increases it increasing geometric sequence if its decreases decreasing the sequence. . \(\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, \ldots\) . b. How can you determine whether a sequence is geometric from its graph? Each week, 40% of the chlorine in the pool evaporates. You sprain your ankle and your doctor prescribes 325 milligrams of an anti-in ammatory drug every 8 hours for 10 days. . Look back at the infinite geometric series in Exploration 1. Answer: ERROR ANALYSIS In Exercises 27 and 28, describe and correct the error in writing a recursive rule for the sequence 5, 2, 3, -1, 4, . Question 3. WHAT IF? . Answer: Question 10. Tn = 180 10 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. MODELING WITH MATHEMATICS What is the 873rd term of the sequence whose first term is a1 = 0.01 and whose nth term is an = 1.01an-1? an = 180/3 = 60 4, 20, 100, 500, . Answer: Question 6. After the first year, your salary increases by 3.5% per year. . In general most of the curve represents geometric sequences. Answer: Write a rule for the nth term of the geometric sequence. State the domain and range. 51, 48, 45, 42, . Writing a Formula d. If you pay $350 instead of $300 each month, how long will it take to pay off the loan? Tn = 1800 degrees. . a12 = 38, a19 = 73 Describe how labeling the axes in Exercises 36 on page 439 clarifies the relationship between the quantities in the problems. Here is what Gauss did: Answer: Question 70. a6 = a6-1 + 26 = a5 + 26 = 100 + 26 = 126. when n = 6 Answer: Write an explicit rule for the sequence. Work with a partner. Write a recursive rule for an = 105 (\(\frac{3}{5}\))n1 . Question 9. Evaluating Recursive Rules, p. 442 For a regular n-sided polygon (n 3), the measure an of an interior angle is given by an = \(\frac{180(n-2)}{n}\) FINDING A PATTERN a6 = 2/5 (a6-1) = 2/5 (a5) = 2/5 x 0.6656 = 0.26624. Given that, \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots\) 1, 4, 5, 9, 14, . 2.00 feet MODELING WITH MATHEMATICS Give an example of a real-life situation which you can represent with a recursive rule that does not approach a limit. 6x = 4 Answer: In Exercises 2938, write a recursive rule for the sequence. What do you notice about the graph of an arithmetic sequence? In Example 6, suppose 75% of the fish remain each year. Question 29. Log in. 1 + x + x2 + x3 + x4 Answer: In Exercises 512, tell whether the sequence is geometric. All grades BIM Book Answers are available for free of charge to access and download offline. 5 + 11 + 17 + 23 + 29 b. . Question 5. You save an additional penny each day after that. Use each formula to determine how many rabbits there will be after one year. Write a rule for the sequence. Work with a partner. a1 = 1 Write a conjecture about how you can determine whether the infinite geometric series . a4 = a3 5 = -9 5 = -14 S39 = 39(-3.7 + 11.5/2) a1 = 2(1) + 1 = 3 Find both answers. an = r . Answer: Question 20. VOCABULARY Question 2. (Hint: L is equal to M times a geometric series.) . 301 = 3n + 1 Draw diagrams to explain why this rule is true. Question 4. For a display at a sports store, you are stacking soccer balls in a pyramid whose base is an equilateral triangle with five layers. 301 = 4 + 3n 3 In Exercises 514, write the first six terms of the sequence. Describe how doubling each term in an arithmetic sequence changes the common difference of the sequence. Justify your answer. Answer: Question 67. D. 5.63 feet b. Given that the sequence is 7, 3, 4, -1, 5. \(\sqrt{x}\) + 2 = 7 Question 15. WHAT IF? Question 2. The library can afford to purchase 1150 new books each year. Question 47. 6n + 13n 603 = 0 You make this deposit each January 1 for the next 30 years. The length2 of the second loop is 0.9 times the length of the first loop. Answer: Question 11. First place receives $200, second place receives $175, third place receives $150, and so on. Answer: Write the series using summation notation. f. 1, 1, 2, 3, 5, 8, . . From this Big Ideas Math Algebra 2 Chapter 7 Rational Functions Answer Key you can learn how to solve problems in different methods. B. an = n/2 Use the sequence mode and the dot mode of a graphing calculator to graph the sequence.