Geometric Sequences pages 427–429 Exercises

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Geometric Sequences pages 427–429 Exercises 1. 4 2. 4 3. 0.1 4. 2.50 ALGEBRA 1 LESSON 8-6 pages 427–429 Exercises 1. 4 2. 4 3. 0.1 4. 2.50 5. –0.25 6. 2 7. 40, 80, 160 8. 48, 96, 192 9. 20.25, 30.375, 45.5625 10. –0.5, 0.25, –0.125 11. 0.36, 0.072, 0.0144 12. –48, 96, –192 13. geometric 14. arithmetic 15. geometric 16. arithmetic 17. arithmetic 18. geometric 19. 5; 135; 10,935 20. –5; –135; –10,935 21. 5; –135; –10,935 22. 0.5; 13.5, 1093.5 23. –2; –250; –156,250 24. –1.1; 70.4; 18,022.4 25. A(n) = 6 • 0.5n–1; 0.375 26. A(n) = –6 • 2n–1; –3072 27. A(n) = 7 • (1.1)n–1; 9.317 28. A(n) = 1 • (-4)n–1; 4096 29. a. A(n) = 100 • (0.64)n–1 b. about 10.74 cm 30. 2 , , ; A(n) = 216 • 31. 1, 0.2, 0.04; A(n) = 625 • (0.2)n–1 2 3 8 9 8 27 1 3 n–1 8-6

35. If all consecutive terms have a common Geometric Sequences ALGEBRA 1 LESSON 8-6 32. 656.1, 5904.9, 53,144.1; A(n) = 0.1 • 9n–1 33. 1, –0.5, 0.25; A(n) = 16 • (–0.5)n–1 34. Check students’ work. 35. If all consecutive terms have a common difference, the sequence is arithmetic. If all consecutive terms have a common ratio, the sequence is geometric. 36. a. 3 folds: 8; 4 folds: 16; 5 folds: 32 b. A(n) = 1 • 2n c. 1024 rectangles 37. arithmetic; 3, 1, –1 38. neither; –3, –8, –14 39. geometric; 1.125, 0.5625, 0.28125 40. arithmetic; 20, 22, 24 41. a. A(n) = 36 • (0.9)n–1 b. 6; n = 1 corresponds to the first swing, because A(1) = 36. c. 21.3 cm 42. a. , , , b. 2–1, 2–2, 2–3, 2–4 c. r = 2–n d. 2–10 or 43. No; if a term were 0, then all terms would be 0 because you multiply a term to get the next term. 1 2 1 4 1 8 1 16 1 210 8-6

(OR equivalent explanation) [1] answer with no work shown n–1 Geometric Sequences ALGEBRA 1 LESSON 8-6 44. a. 1, , , b. r = 1 • c. d. 0, , , e. r = 1 – 1 • f. 45. x; x5, x6, x7 46. 3x; 27x4, 81x5, 243x6 47. xy2; x5y9, x6y11, x7y13 48. ab; 2a4b2, 2a5b3, 2a6b4 3 4 9 16 27 64 49. 6  10–2; 2.592  102, 1.5552  101, 9.3312  10–1 50. 5th 51. D 52. H 53. B 54. [2] Day 1 350 Day 2 700 Day 3 1400 Day 4 2800 Day 5 5600 (OR equivalent explanation) [1] answer with no work shown 3 4 n–1 243 1024 1 4 7 16 37 64 3 4 n–1 14,197 16,384 8-6

Geometric Sequences 55. a4 66. y = – x 56. 16 67. y = – x 57. ALGEBRA 1 LESSON 8-6 55. a4 56. 16 57. 58. 1 59. 60. 61. 62. 63. 2.467  10–3 64. 3.26  1011 gal 65. y = x 66. y = – x 67. y = – x 68. y = x 69. y = x 70. y = – x 71. y = x 72. y = – x 2 5 7 6 1 x10z20 5 3 7 4 81 64 1 4 1 m14 5 9 1 p15 1 2 d 5 c 2 8 3 8-6