Describing Number Patterns ALGEBRA 1 LESSON 5-6 pages 270–273 Exercises 1. “Add 2 to the previous term”; 12, 14. 2. “Multiply the previous term by 1 ”; 20 , 30 . 3. “Add 2 to the first term, 3 to the second term and continue, adding 1 more each time”; 18, 24. 4. “Add 0.04 to the previous term”; 3.16, 3.20. 5. “Multiply the previous term by 1.1”; 4.3923, 4.83153. 6. “Add –2 to the previous term”; –5, –7. 7. “Add 1.1 to the previous term”; 5.5, 6.6. 8. “Multiply the previous term by 10”; 10, 100. 9. “Multiply the previous term by 4”; 512, 2048. 10. “Square the reciprocals of consecutive integers”; , . 11. “Add –14 to the previous term”; –47, –61. 12. “Multiply the previous term by 5”; 937.5, 4687.5. 13. 3 14. –4 15. –11 16. 13 17. – 18. 0.8 19. –2 20. 12 21. 5 22. 5, 14, 26 23. –3, 15, 39 24. –3, 9, 25 1 2 1 4 3 8 1 6 1 25 1 36 5-6
Describing Number Patterns ALGEBRA 1 LESSON 5-6 25. 17, 44, 80 26. 3.5, 12.5, 24.5 27. 2, 23, 51 28. 3, –15, –39 29. –7.1, –22.1, –42.1 30. 58, 37, 9 31. 17, 5, –11 32. –8, –17, –29 33. –0.8, –3.8, –7.8 34. –4, –10 35. 3 , 3 36. 26, 37 37. , 38. 35, 48 39. 31, 40 40. 2.5, 1.25 41. 8, 8 42. , – 43. a. Answers may vary. Sample: Inductive reasoning is making conclusions based on patterns, while deductive reasoning is making conclusions based on given facts. b. Answers may vary. Check students’ work. 4 27 4 81 44. 5 min 45. Answers may vary. Sample: A(n) = 2 – 4n 46. 7 lb 4 oz, 7 lb 9 oz, 7 lb 14 oz, 8 lb 3 oz, 8 lb 8 oz; the baby’s weight at the end of the 4th week 47. $4500, $4350, $4200, $4050, $3900; the balance after 4 payments 1 4 4 27 4 81 1 4 1 2 5-6
Describing Number Patterns ALGEBRA 1 LESSON 5-6 56. 11 , 12, 13 57. 4.5, –4.5, –22.5 58. –2, –5.2, –11.6 59. 1, 2 , 5 60. a. 11, 14 b. c. The points lie on a line. 1 3 1 3 48. a. 1 2 4; 7 1 2 b. = 2; = 2; 8 c. When there are more than three terms you can test the pattern to make sure it is reasonable. 49. No; there is no common difference. 50. Yes; the common difference is –4. 51. No; there is no common difference. 52. No; there is no common difference. 53. Yes; the common difference is –15. 54. Yes; the common difference is –0.8. 55. a. 1, 5, 10, 10, 5, 1 b. 1, 2, 4, 8, 16; 32 ) ) 2 1 4 2 3 5 4 5 5-6
Describing Number Patterns ALGEBRA 1 LESSON 5-6 66. value of new term = value of previous term + 4 67. value of new term = value of previous term ÷ 7 68. value of new term = value of previous term • (–2.5) 69. x; 4x + 4 70. 3a + 2b; 10a + 7b + c 71. a. 10 b. –6 c. A(n) = 10 + (n – 1)(–6) 61. a. Yes; for each input there is only one output value. b. For every increase of 7 in the key position, the frequency doubles. 62. a. 21 b. 89 c. Answers may vary. Sample: 3, 3, 6, 9, 15, 24, 39 63. value of new term = value of previous term + 6 64. value of new term = value of previous term • 1.5 65. value of new term = value of previous term – 2.5 5-6
Describing Number Patterns ALGEBRA 1 LESSON 5-6 72. a. b. Blue; the colors rotate red, blue, and purple. Every third figure is purple. Since 21 is divisible by 3, the 21st figure is purple. The figure just before a purple figure is blue. c. 12 sides; the figures show this pattern for number of sides. Figure Number of Sides 1–3 3 4–6 4 7–9 5 10–12 6 13–15 7 16–18 8 19–21 9 22–24 10 25–27 11 28 12 5-6
Describing Number Patterns ALGEBRA 1 LESSON 5-6 73. a. –5 b. 6 c. A(n) = –5 + (n – 1)(6) 74. C 75. F 76. A 77. H 78. C 79. H 80. [2] The common difference is –3. The seventh term is 24 + (7 – 1)(–3) = 6. [1] explanation incomplete 81. [4] a. ƒ(n) = 26,500 + 2880n b. 2008 is 7 years after 2001. ƒ(7) = 26,500 + (2880)(7) = $46,660 Marta’s 2008 salary is $46,660. [3] function and salary found but work not shown [2] minor computation error in finding salary [1] function shown but salary not found 82. y = – x 83. y = 24x 84. y = –14x 85. y = 0.14x 86. y = – x 87. y = – x 5 4 31 11 31 110 5-6
Describing Number Patterns ALGEBRA 1 LESSON 5-6 88. y = – x 89. y = x 90. {–20, –4, 8} 91. {–19, –3, 9} 92. {–2, 7, 19} 93. {2, 4, 10} 94. {2, 4, 10} 95. {–6 , –4 , –1 } 96. a. about 84% b. about 11% 3 2 2 3 1 2 1 4 1 4 5-6