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LESSON
7.2
Answers for the lesson “Analyze Arithmetic
Sequences and Series”
Skill Practice
1. common difference
2. An arithmetic sequence is a list
of numbers that have the same
common difference between
consecutive terms. An arithmetic
series is the sum of the terms of
the arithmetic sequence.
3. Arithmetic; there is a common
difference of 3 between
consecutive terms.
4. Not arithmetic; there is not a
common difference between
consecutive terms.
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5. Arithmetic; there is a common
difference of 9 between
consecutive terms.
6. Not arithmetic; there is not a
common difference between
consecutive terms.
7. Arithmetic; there is a common
difference of 0.5 between
consecutive terms.
8. Not arithmetic; there is not a
common difference between
consecutive terms.
9. Not arithmetic; there is not a
common difference between
consecutive terms.
10. Not arithmetic; there is not a
common difference between
consecutive terms.
11. Arithmetic; there is a common
difference of 1.5 between
consecutive terms.
12. an 5 3n 2 2; 58
13. an 5 21 1 6n; 119
14. an 5 25 1 13n; 255
15. an 5 25 1 2n; 35
16. an 5 10 2 4n; 270
17. an 5 36 2 11n; 2184
2
2 38
18. an 5 2} 1 }n; }
3
3 3
7
13
1
19. an 5 } 2 }n; 2}
3
3
3
20. an 5 20.6 1 2.1n; 41.4
21. The equation for an arithmetic
sequence is not correct;
an 5 a1 1 (n 2 1)d,
an 5 37 1 (n 2 1)(213),
an 5 50 2 13n.
22. The terms were substituted
into the wrong places;
37 5 (n 2 1)(213),
an 5 50 2 13n.
23. an 5 228 1 5n; points at
(1, 223), (2, 218), (3, 213),
(4, 28), (5, 23), (6, 2)
Algebra 2
Answer Transparencies for Checking Homework
208
24. an 5 270 1 9n; points at
(1, 261), (2, 252), (3, 243),
(4, 234), (5, 225), (6, 216)
25. an 5 152 2 14n; points at
(1, 138), (2, 124), (3, 110),
(4, 96), (5, 82), (6, 68)
26. an 5 81 2 7n; points at
(1, 74), (2, 67), (3, 60), (4, 53),
(5, 46), (6, 39)
7
27. an 5 25 1 }n; points at
2
(1, 21.5), (2, 2), (3, 5.5), (4, 9),
(5, 12.5), (6, 16)
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1
28. an 5 6 2 }n; points at
2
(1, 5.5), (2, 5), (3, 4.5), (4, 4),
(5, 3.5), (6, 3)
29. C
30. an 5 25 1 9n
31. an 5 9 1 5n
32. an 5 211 1 3n
33. an 5 22 2 4n
34. an 5 17 1 8n
35. an 5 13 1 2n
13
111
36. an 5 } 2 }n
5
5
15
9
37. an 5 } 1 }n
4
4
12
2
38. an 5 } 2 }n
5
5
39. B
40. 175
41. 296
42. 2774
43. 2585
44. 252
45. 315
46. 450
47. 132
48. 161
49. an 5 23 1 5n
50. an 5 2 2 3n
51. an 5 21 2 2n
52. Sample answer: The graph of
a n is just points at every integer
n and the graph of f(x) is a line.
Both graphs have the same rate of
change between points.
53. False. Sample answer: Doubling
the common difference alone does
not double the sum.
54. true; a 1 c 5 2b
55. 12
56. 8
57. 25
58. 5
59. 15
60. 9
61. 22,500
8
2
62. }, 2}
3
3
Problem Solving
63. a. an 5 6n
b. 271 cells
Algebra 2
Answer Transparencies for Checking Homework
209
64. an 5 1 1 2n; 63 band members
65. a. an 5 24 1 8n
or 343 ft
n d(n)
1
16
2
48
3
80
4
112
d. Sample answer: A roll with a
diameter of 7 in. requires 625
wraps and contains 8828 in. of
paper. This is about 2.14 times
as much paper as the 5 in. roll,
so you would expect a cost of
about 2.14($1.50) = $3.21.
b. an 5 216 1 32n
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66. c.
*n 5 [2 1 0.008(n 2 1)]:
c. 375 times; about 4119 in.,
b. 576 blocks
66. a.
b. arithmetic;
2y
69. a1 5 }
n 2x
d(n)
12
21
n
67. $100
68. a.
n dn (in.)
*n (in.)
1
2
2:
2
2.008
2.008:
3
2.016
2.016:
4
2.024
2.024:
Algebra 2
Answer Transparencies for Checking Homework
210