Study Guide and Review - Chapter 10. Find the indicated term of each arithmetic sequence. 11. a 1. = 9, d = 3, n = 14
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1 Find the indicated term of each arithmetic sequence. 11. a 1 = 9, d = 3, n = 14 Substitute 9 for a 1, 3 for d, and 14 for n in the 14. a 1 = 1, d = 5, n = 18 Substitute 1 for a 1, 5 for d, and 18 for n in the Find the arithmetic means in each sequence ,,,, a 1 = 3, d = 6, n = 22 Substitute 3 for a 1, 6 for d, and 22 for n in the Substitute 12 for a 1, 5 for n, and 8 for a 5 in the formula for the nth term and find d. 13. a 1 = 10, d = 4, n = 9 The arithmetic means are ( ) or 7, ( 7 + 5) or 2 and ( 2 + 5) or 3. Substitute 10 for a 1, 4 for d, and 9 for n in the esolutions Manual - Powered by Cognero Page 1
2 16. 15,,, ,,,, 24 Substitute 15 for a 1, 4 for n, and 29 for a 4 in the formula for the nth term and find d. Substitute 72 for a 1, 5 for n, and 24 for a 5 in the formula for the nth term and find d. The arithmetic means are The arithmetic means are (72 12) or 60, (60 12) or 48 and (48 12) or ,,,,, BANKING Carson saves $40 every 2 months. If he saves at this rate for two years, how much will he have at the end of two years? Substitute 12 for a 1, 6 for n, and 8 for a 6 in the formula for the nth term and find d. Substitute 40 for a 1, 12 for n and 40 for d in the formula for the nth term and find a 12. The arithmetic means are (12 4) or 8, (8 4) or 4, (4 4) or 0 and (0 4) or 4. esolutions Manual - Powered by Cognero Page 2
3 Find S n for each arithmetic series a 1 = 16, a n = 48, n = 6 Substitute 16 for a 1, 48 for a n, 6 for n in the Sum Substitute 9 for a 1, 5 for d, and 74 for a n in the formula for the nth term and find n. Substitute 9 for a 1, 74 for a n, 14 for n in the Sum 21. a 1 = 8, a n = 96, n = 20 Substitute 8 for a 1, 96 for a n, 20 for n in the Sum esolutions Manual - Powered by Cognero Page 3
4 Substitute 16 for a 1, 9 for d, and 65 for a n in the formula for the nth term and find n. 24. DRAMA Laura has a drama performance in 12 days. She plans to practice her lines each night. On the first night she rehearses her lines 2 times. The next night she rehearses her lines 4 times. The third night she rehearses her lines 6 times. On the eleventh night, how many times has she rehearsed her lines? The arithmetic sequence that represents the situation is 2, 4, 6, Substitute 2 for a 1, 2 for d, and 11 for n in the formula for the nth term and find a 11. Substitute 16 for a 1, 65 for a n, 10 for n in the Sum Substitute 2 for a 1, 22 for a n, 11 for n in the Sum esolutions Manual - Powered by Cognero Page 4
5 Find the sum of each arithmetic series Use the formula. There are 17 terms, a 1 = 3(5) 2 or 13, and a 21 = 3 (21) 2 or 61. Use the formula. There are 9 terms, a 1 = 2(4) + 5 or 3, and a 9 = 2 (12) + 5 or 19. Find the indicated term for each geometric sequence a 1 = 5, r = 2, n = 7 Use the formula. Substitute 5 for a 1, 2 for r, 7 for n in the formula for the nth term and simplify. There are 11 terms, a 1 = 6(0) 1 or 1, and a 11 = 6 (10) 1 or 59. The seventh term is 320. esolutions Manual - Powered by Cognero Page 5
6 29. a 1 = 11, r = 3, n = a 8 for Substitute 11 for a 1, 3 for r, 3 for n in the formula for the nth term and simplify. Find the common ratio r. The third term is 99. Substitute for a 1, 3 for r, 8 for n in the formula for the nth term and simplify. 30. Substitute 128 for a 1, for r, 5 for n in the The eighth term is. Find the geometric means in each sequence. The fifth term is ,,, 162 Substitute 6 for a 1, 162 for a 4, 4 for n in the formula for the nth term and find r. The geometric means are 6(3) or 18 and 18(3) or 54. esolutions Manual - Powered by Cognero Page 6
7 33. 8,,,, 648 Substitute 8 for a 1, 648 for a 5, 5 for n in the formula for the nth term and find r. 35. SAVINGS Nolan has a savings account with a current balance of $1500. What would be Nolan s account balance after 4 years if he receives 5% interest annually? Substitute 1500 for a 0, 1.05 for r and 4 for n in the formula and simplify. The geometric means are 8(±3) or ±24, ±24(±3) or 72 and 72(±3) or ± ,,, 108 Find S n for each geometric series. 36. a 1 = 15, r = 2, n = 4 Substitute 4 for a 1, 108 for a 4, 4 for n in the formula for the nth term and find r. Substitute 15 for a 1, 2 for r, 4 for n in the Sum The geometric means are 4( 3) or 12 and 12( 3) or 36. esolutions Manual - Powered by Cognero Page 7
8 37. a 1 = 9, r = 4, n = to 5 terms Substitute 9 for a 1, 4 for r, 6 for n in the Sum Find the common ratio r. Substitute 243 for a 1, for r, 5 for n in the Sum to 7 terms Find the common ratio r. Substitute 5 for a 1, 2 for r, 7 for n in the Sum 40. Evaluate the sum of each geometric series. Substitute 3 for a 1, 2 for r, 7 for n in the Sum esolutions Manual - Powered by Cognero Page 8
9 41. Substitute 1 for a 1, for r, 8 for n in the Sum 42. ADVERTISING Natalie is handing out fliers to advertise the next student council meeting. She hands out fliers to 4 people. Then, each of those 4 people hand out 4 fliers to 4 other people. Those 4 then hand out 4 fliers to 4 new people. If Natalie is considered the first round, how many people will have been given fliers after 4 rounds? Substitute 1 for a 1, 4 for r, 4 for n in the Sum Therefore, 85 people will have been given flier after 4 rounds. esolutions Manual - Powered by Cognero Page 9
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