Name Class Date Extra Practice
Chapter 9
Lesson 9-1
Write a recursive definition for each sequence.
1. 3, 5, 7, . . . a1 5 3, an 5 an21 1 2
4. 0.2, 0.5, 0.8, . . .
a1 5 0.2, an 5 an21 1 0.3
2. 19, 15, 11, . . .
a1 5 19, an 5 an21 2 4
5. 223, 236, 249, . . .
a1 5 223, an 5 an21 2 13
3. 212, 210.5, 29, . . .
a1 5 212, an 5 an21 1 1.5
6. 25, 37.5, 50, . . .
a1 5 25, an 5 an21 1 12.5
Decide whether each formula is explicit or recursive. Then find the first five
terms of each sequence.
7. an 5 3n 1 2
8. a1 5 4; an 5 an21 1 7
explicit; 5, 8, 11, 14, 17
recursive; 4, 11, 18, 25, 32
10. a1 5 2; an 5 an21 2 3
11. an 5 6n 2 2 1
recursive; 2, 2 1, 2 4, 2 7, 2 10
explicit; 5, 23, 53, 95, 149
9. an 5 5n(n 1 2)
explicit; 15, 40, 75, 120, 175
12. an 5 6 2 2n
explicit; 4, 2, 0, 2 2, 2 4
13. A contractor must pay a penalty if work on a project is not completed on
time. The penalty on the first day is $300. The penalty increases to $500
on the second day, to $700 on the third day, and so on.
a. Write an explicit formula that describes the sequence.
an 5 100 1 200n
b. The contractor accumulated a penalty of $4500. How many days after the
due date was the project completed? 22 days
14. Table tennis rules regulate the specific properties for the table, the ball, the
net, and the paddles. According to the rules, a ball dropped from 30 cm above
the table surface must bounce back to the height of 23 cm. This ratio of the
drop height to the bounce height remains the same for any two consecutive
bounces.
a. Write the first five terms of a sequence that describes the bounce heights
after an initial drop of 30 cm. Round your answers to the nearest tenth.
23 cm, 17.6 cm, 13.5 cm, 10.4 cm, 7.9 cm
n
an 5 30 Q 23
b. Write an explicit formula that describes the sequence.
30 R
Lesson 9-2
Determine whether each sequence is arithmetic. If so, identify the common difference.
15. 5, 9, 13, 17, . . . yes; 4
16. 7, 1, 25, 211, . . . yes; 26
17. 9, 218, 27, 236, . . . no
18. 15, 12, 9, 6, . . . yes; 23
19. 2, 5, 9, 14, . . .
20. 212, 25, 2, 9, . . . yes; 7
no
Find the 24th term of each sequence.
21. 9, 12, 15, 18, . . . 78
22. 19, 12, 5, 22, . . . 2142
24. 43, 41, 39, 37, . . .23
25. 216, 24, 8, 20, . . . 260
23. 2187, 2181, 2175, 2169, . . .
249
26. 0.40, 0.35, 0.30, 0.25, . . . 20.75
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Name Class Date Extra Practice (continued)
Chapter 9
Find the arithmetic mean an of the given terms.
27. an21 5 10, an11 5 20
15
28. an21 5 7, an11 5 19
13
29. an21 5 22, an11 5 27
24.5
30. a.Find the common difference for the arithmetic sequence that has 17 as its
twelfth term and 71 as its sixth term. 29
b. Write the explicit formula for the sequence.
an 5 125 2 9n
Lesson 9-3
Find the eighth term of each geometric sequence.
31. 2, 6, 18, . . . 4374
32. 27, 21, 263, . . . 15,309
1 1
33. 12, 2, 3, . . . 23,328
Write an explicit formula for each geometric sequence. Then generate the first
five terms.
1
35. a1 5 227, r 5 3 34. a1 5 6, r 5 2 an 5
6(2)n21;
6, 12, 24, 48, 96
n21
an 5 227 Q 13 R
;
1
29, 23, 21, 23
36. a1 5 1900, r 5 0.1
227,
37. a1 5 25, r 5 3
38. a1 5 1, r 5 4 an 5 25(3)n21;
an 5 4n21;
25, 215, 245, 2135, 2405
1, 4, 16, 64, 256
an 5 1900(0.1)n21;
1900, 190, 19, 1.9, 0.19
39. a1 5 500, r 5 0.2
an 5 500(0.2)n21;
500, 100, 20, 4, 0.8
40. A fruit fly receives genetic material from two parents. Each parent also
receives genetic material from 2 parents. So each fruit fly receives genes from
4 grandparents, 8 great-grandparents, and so on. How many ancestors does a
fruit fly have going back 15 generations?
65,534 ancestors
Lesson 9-4
Find the sum of each finite arithmetic series.
41. 3 1 5 1 7 1 9 1 11
35
42. 13 1 9 1 5 1 1 1 (23)
25
43. 4 1 11 1 18 + . . . 1 53
228
44. (22) 1 3 1 8 1 . . . 1 23
63
3
5
1
11
45. 2 1 2 1 2 1 . . . 1 2 18
46. (25) 1 (21) 1 3 1 . . . 1 15
30
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Name Class Date Extra Practice (continued)
Chapter 9
Write each arithmetic series in summation notation. Then evaluate each series.
47. 21, 19, 17, 15, . . . ; 8 terms
48. 4, 7, 10, 13, 16, 19, . . . ; 10 terms
a (22n 1 23); 112
a (3n 1 1); 175
8
10
n51
n51
49. 235, 228, 221, 214, . . . ; 7 terms
50. 97, 96, 95, 94, 93, . . . ; 20 terms
a (7n 2 42); 298
a (2n 1 98); 1750
7
20
n51
n51
Find the sum of each finite series.
51. a (2n 1 3) 45
5
n51
52. a (4 2 n) 2 3
7
n52
53. a (n 1 1)
5
20
n51
54. The orchestra section of a theater has 25 seats in the front row, 27 seats in the
second row, 29 seats in the third row, and so on. The pattern continues until
the twelfth row. After that, every row has the same number of seats as row 12.
a. How many seats are there in row 12?
47 seats
b. The orchestra section has 19 rows. How many seats are in the
orchestra section? 761 seats
Lesson 9-5
Evaluate the sum of the finite geometric series.
55. 1 1 2 1 4 1 . . . ; n 5 8 255
56. 3 1 6 1 12 1 . . . ; n 5 7 381
57. 243 2 81 1 27 2 3 1 . . . ; n 5 8 1640
9
1
1
58. 27 1 3 1 3 1 . . . ; n 5 7 597,871
27
59. 25 2 15 2 45 2 . . . ; n 5 6 2728
625
60. 20 2 50 1 125 2 2 1 . . . ; n 5 9
1,395,455
64
Determine whether each infinite geometric series diverges or converges.
If it converges, state the sum.
1
61. 4 1 2 1 1 1 2 1 . . .
converges, 8
1
1
62. 3 2 1 1 3 2 9 1 . . .
63. 2.2 2 0.22 1 0.022 2 . . .
converges, 94
5
5
5
64. 0.9 1 0.09 1 0.009 1 . . . 65. 5 2 2 1 4 2 8 1 . . .
converges, 1
converges, 10
3
converges, 2
66. 1 1 0.1 1 0.01 1 . . .
converges, 10
9
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Name Class Date Extra Practice (continued)
Chapter 9
Determine whether each series is arithmetic or geometric. Then evaluate the
finite series for the specified number of terms.
67. 3 1 6 1 9 1 12 1 15 1 . . . ; 10th term
arithmetic; 165
68. 3 1 6 1 12 1 24 1 48 1 . . . ; 10th term
geometric; 3069
69. 21000 1 500 2 250 1 125 2 . . . ; 7th term 70. 87 1 72 1 57 1 42 1 . . . ; 20th term
geometric; 2 671.875
arithmetic; 2 1110
71. Give an example of an infinite geometric series without a finite sum.
Answers may vary. Sample: 2 1 4 1 8 1 16 1 . . .
4
72. Suppose a dropped ball bounces back to 5 of its original height. A ball falls
from a height of 5 feet and keeps bouncing until someone picks it up. Estimate
the total vertical distance the ball travels if no one picks it up. 45 ft
73. A new company hires an executive. The company is not expected to make a
profit right away, so the executive agrees to an alternative payment scheme.
The first month, he receives $.01. Each successive month his salary doubles,
until his annual salary equals or exceeds $2,000,000. Then this salary remains
at the maximum level.
a. What is the total salary the executive receives in the first year?
$40.95
b. After how many months will the company start paying the executive the
maximum salary under the contract?
25
c. According to the contract, what is the maximum annual salary? $2,013,265.92
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