Write the first five terms of each arithmetic sequence. See Example 2.
- , 8. ,
- , 10. ,
Use the formula for to find the general term of each arithmetic sequence. See Example 3.
- , 12. , 13.3, , ,
14.1, 15. 16.
Evaluate the indicated term for each arithmetic sequence. See Examples 3 and 5.
- , ; 18. , ;
- ; 20. ;
- , ; 22. , ;
Evaluate the number of terms in each arithmetic sequence. See Example 6.
- 24.4, 1,
25. , 3, 26.2, , 1,
27.Concept Check In the formula for , what does nrepresent?
28.Explain when you would use each of the two formulas for.
Evaluate for each arithmetic sequence. See Examples 7 and 8.
- , 30. , 31. ,
- , 33. 34.
Use a formula for to evaluate each series. See Example 9.
35. 36. 37.
38. 39. 40.
Solve each problem. (Hint: Immediately after reading the problem, determine whether you
need to find a specific term of a sequence or the sum of the terms of a sequence.)See
Examples 4, 7, 8, and 9.
41.Nancy Bondy’s aunt has promised to deposit $1 in her account on the first day of her
birthday month, $2 on the second day, $3 on the third day, and so on for 30 days. How
much will this amount to over the entire month?
42.Repeat Exercise 41,but assume that the deposits are $2, $4, $6, and so on, and that the
month is February of a leap year.
43.Suppose that Cherian Mathew is offered a job at $1600 per month with a guaranteed in-
crease of $50 every six months for 5 yr. What will Cherian’s salary be at the end of that
time?
44.Repeat Exercise 43,but assume that the starting salary is $2000 per month and the guar-
anteed increase is $100 every four months for 3 yr.
a
2000
i= 1
a^ i
250
i= 1
a^ i
11
i= 1
a
1
2
i- 1 b
a
20
i= 1
a
3
2
a^ i+^4 b
17
i= 1
a^13 i-^12
10
i= 1
18 i- 52
Sn
a 1 =- 5 d=- 4 an= 4 + 3 n an= 9 + 5 n
a 1 = 6 d= 3 a 1 = 5 d= 4 a 1 = 7 d=- 3
S 6
Sn
Sn
- 5
1
2
,Á,
3
2
21
4
,Á, 12
3
4
3, 5, 7,Á, 33 -2,Á, - 32
a 12 =- 45 a 10 =- 37 a 1 a 10 =- 2 a 15 =- 8 a 3
2, 4, 6,Á a 24 1, 5, 9,Á a 50
a 1 = 4 d= 3 a 25 a 1 = 1 d=- 3 a 12
- 3, 0, 3,Á -10, -5, 0,Á
5
3
,
7
3
, 3,Á
21
4
,Á
9
2
15
4
a 1 = 2 d= 5 a 1 = 5 d= 3
an
a 1 =- 2 d=- 4 a 1 =- 3 d=- 5
a 1 = 5 d= 4 a 1 = 6 d= 7
690 CHAPTER 12 Sequences and Series
