ANSWERS A-15 SECTION 5.7, PAGE 280 1. Sequence 3. Arithmetic 5. Geometric 7. 5, 7, 9, 11, 13 9. 15, 11, 7, 3, 1 − − − − − 11. 5, 3, 1, 1, 3 − − 13. 63 15. 127 17. 64 − 19. a n n = 21. a n2 1 n = − 23. a n3 2 n = + 25. 1275 27. 2500 29. 340 31. 2, 6, 18, 54, 162 33. 5, 10, 20, 40, 80 35. 3, 3, 3, 3, 3 − − − 37. 96 39. 1,048,576 − 41. 3645 − 43. a 4 n n = 45. a 2 1 2 n n 1 = ⋅ ⎛ ⎝⎜ ⎞ ⎠⎟ − 47. a 16 1 2 n n 1 = − ⋅ ⎛ ⎝⎜ ⎞ ⎠⎟ − 49. 189 51. 4095 − 53. 14,348,906 55. 5050 57. 10,100 59. 78 times 61. a) 63 in. b) 954 in. 63. 15,992 students 65. $68,066.54 67. 69.65 million people 69. 161.4375 71. 267 73. 191.3568 ft 74. a) $320, $310 b) $10,240; $10,230 c) It is risky because it is likely that you won’t have enough money to continue doubling your previous bet if you lose several times in a row. Also, there may be a maximum amount you can bet in a game of chance. SECTION 5.8, PAGE 287 1. Fibonacci 3. Divine 5. Ratio 7. Yes; 29, 47 9. No 11. Yes; 3, 5 13. Yes; 105, 170 15. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 17. Answers will vary. 19. Answers will vary. 21. a) Answers will vary. b) Answers will vary. 23. The sums of the numbers along the diagonals (parallel to the one shown) are Fibonacci numbers. 25. a) 1.618 b) 0.618 c) 1 27. Answers will vary. 29. The decimal expansion shows several terms of the Fibonacci sequence. 31. The ratio of the second to the first, and the fourth to the third measures estimates the golden ratio. 33. Answers will vary. 35. a) Answers will vary. b) Answers will vary. c) Answers will vary. REVIEW EXERCISES, PAGE 290 1. 2, 3, 4, 5, 6, 10 2. 2, 3, 4, 6, 9 3. 2 3 5 2 3 ⋅ ⋅ 4. 2 3 11 2 2 ⋅ ⋅ 5. 15; 210 6. 9; 756 7. 180 minutes 8. 1− 9. 3 10. 6− 11. 4− 12. 9− 13. 3 14. 21 − 15. 24 16. 5 17. 2− 18. 20 19. 12 − 20. 35 21. 2738 − 22. 0.3 23. 3.75 24. 0.857142 25. 0.583 26. 54 10 27 5 = 27. 2 3 28. 51 99 17 33 = 29. 83 1000 30. 49 9 31. 13 4 − 32. 6 1 3 33. 27 1 5 − 34. 2 15 − 35. 17 12 36. 1 4 37. 35 54 38. 17 33 39. 9 20 40. 13 15 41. 13 34 21. No 23. No 25. Yes 27. No 29. Commutative property of addition. The only difference between the expressions on both sides of the equal sign is the order of 5 and x. 31. No. 3 4 4 3 ÷ ≠ ÷ 33. ( 3)( 4) ( 4)( 3) 12 − − = − − = 35. (2) (3) (4) (2) (3) (4) 9 [ ] [ ] −+− +−=−+−+− =− 37. No. (16 8) 2 16 (8 2). ÷ ÷ ≠ ÷ ÷ 39. No. (81 9) 3 81 (9 3). ÷ ÷ ≠ ÷ ÷ 41. Distributive property 43. Associative property of multiplication 45. Associative property of addition 47. Commutative property of multiplication 49. Distributive property 51. Commutative property of addition 53. b2 10 + 55. c3 21 − 57. x5 1 − + 59. x2 1 − 61. 2 63. 5 2 5 3 + 65. No. a a 0 0 (when 0), ÷ = ≠ but a 0 ÷ is undefined. 66. 2 2 3 1 4 4 1 2 3 1 4 3 2 3 2 4 1 22 24 243 32 71 51 12 67. a) No b) No c) Answers will vary. SECTION 5.6, PAGE 272 1. x5 3. 1 5. x6 7. a) 1024 b) 1024 − 9. a) 9 b) 9 11. a) 1 b) 1− 13. a) 1 b) 6 15. a) 1 27 b) 1 49 17. a) 1 81 − b) 1 81 19. a) 64 b) 729 21. a) 4 b) 1 16 23. 6.32 105 × 25. 3.2 10 3 × − 27. 5.6 10 1 × − 29. 1.9 104 × 31. 1.86 10 4 × − 33. 4400 35. 0.000293 37. 0.0000862 39. 2.01 41. 1,440,000 43. 0.0153 45. 250 47. 0.0021 49. 7.2 108 × 51. 4.5 10 7 × − 53. 7.0 101 × 55. 2.0 10 7 × − 57. 3.6 10 ; 1.7; 9.8 10 ; 1.03 10 3 2 4 × × × − 59. 8.3 10 ; 0.00079; 4.1 10 ; 40,000 5 3 × × − 61. a) $68,018.58 b) $27,263.32 63. 0.042 65. $77,863.50 67. 11.95 hours 69. 8.64 10 ft 9 3 × 71. 2.9 108 × cells 73. 333,333 times 75. 1000 77. 5,821,000 people 79. a) 1 10,1 10,1 10 6 9 12 × × × b) 1000 days (about 2.74 years) c) 1,000,000 days (about 2739.73 years) d) 1,000,000,000 days (about 2,739,726.03 years) e) 1000 times greater 81. a) 1024 bacteria b) 1448 bacteria
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