College Algebra 9th txtbk

SECTION 8–1 Sequences and Series 509
ANSWERS TO MATCHED PROBLEMS
1. 1, 1, 0, 1, 1, 2, 3 2. (A) a n 2n (B) a n (1) n1 a 1 n1
2 b
5
4
3. 4. (A) a (1) k1 a 2 k1
1 1 3 1 5 1 7 1 9 1 11
(B)
3 b a
k 1
k 0
(1) k a 2 3 b k
8-1 Exercises
1. Explain the difference between a sequence and a series.
2. What is a recursion formula?
3. Explain how the Fibonacci sequence can be defined by means
of a recursion formula.
4. Explain summation notation.
5. Explain why the following statement is not true: The general
term of the sequence 1, 3, 7, . . . is 2 n 1.
6. Explain why at least one term must be provided when defining
a sequence recursively.
Write the first four terms for each sequence in Problems 7–12.
7. a n n 2 8. a n n 3
9. a n n 1
n 1
10. a n a1 1 n
n b
11. a n (2) n1 12.
13. Write the eighth term in the sequence in Problem 7.
14. Write the tenth term in the sequence in Problem 8.
15. Write the one-hundredth term in the sequence in Problem 9.
16. Write the two-hundredth term in the sequence in Problem 10.
In Problems 17–22, write each series in expanded form without
summation notation.
5
k 1
4
k 1
6
21. a (1) k
22. a (1) k1 k
k 1
a n (1)n1
n 2
17. a k
18. a
k 1
k 1
3
5
19. 20. a a 1 k
1
a
10 3 b k
k 1
Write the first five terms of each sequence in Problems 23–32.
25. a n 1 3 a1 1
10 nb 26. a n n[1 (1) n ]
23. a n (1) n1 n 2 24. a n (1) n1 a 1 2 nb
4
k 2
27. a 28. a n ( 3 2) n1
n ( 1 2) n1
29. a 1 7; a n a n1 4, n 2
30. a 1 3; a n a n1 5, n 2
31. a 1 4; a n 1 4a n1 , n 2
32. a 1 2; a n 2a n1 , n 2
In Problems 33–36, write the first seven terms of each sequence.
33. a 1 1, a 2 2, a n a n2 2a n1 , n 3
34. a 1 1, a 2 1, a n a n2 a n1 , n 3
35. a 1 1, a 2 2, a n 2a n2 a n1 , n 3
36. a 1 2, a 2 1, a n a n2 a n1 , n 3
In Problems 37–48, find a general term a n for the given sequence
a 1 , a 2 , a 3 , a 4 , . . .
37. 2, 1, 0, 1, . . . 38. 10, 11, 12, 13, . . .
39. 5, 7, 9, 11, . . . 40. 1, 1, 3, 5, . . .
41. 1, 1, 1, 1, . . . 42. 1, 1 2, 1 3, 1 4, . . .
43. 2, 3 2, 4 3, 5 4, . . .
1
44. 3, 2 4, 3 5, 4 6, . . .
47. x, x2
48. x, x 3 , x 5 , x 7 , . . .
2 , x3
3 , x4
4 , . . .
45. 3, 9, 27, 81, . . . 46. 5, 25, 125, 625, . . .
In Problems 49–54:
(A) Find the first four terms of the sequence.
(B) Find a general term b n for a different sequence that has the
same first three terms as the given sequence.
49. a n n 2 n 2 50. a n 9n 2 21n 14
51. a n 6n 2 11n 6 52. a n 25n 2 60n 36
53. a n 2n 2 8n 7 54. a n 4n 2 15n 12
In Problems 55–58, use a graphing calculator to graph the first
20 terms of each sequence.
55. a n 1n 56. a n 2 n
57. a n (0.9) n 58. a 1 1, a n 2 3 a n1 1 2