1. 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 ,
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”; ,
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,
13. 3
14. –4
15. –11
16. 13
17. –
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
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2. Describing Number Patterns
ALGEBRA 1 LESSON 5-6
25. 17, 44, 80
, 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
, 3
36. 26, 37 ,
38. 35, 48
39. 31, 40
, 1.25
41. 8, 8
, –
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
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3. Describing Number Patterns
ALGEBRA 1 LESSON 5-6
, 12, 13
, –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
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
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4. 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

5. 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
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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, n
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
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7. 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