698 CHAPTER 12 Sequences and Series
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12.3 EXERCISES
If the given sequence is geometric, find the common ratio r. If the sequence is not geometric,
say so. See Example 1.1.4, 8, 16, 32, 2.5, 15, 45, 135, 3. , , , ,4. , , , 2, 5.1, 9, 81, 6.2, 32,
7.1, , , , 8. , , , ,
Find a general term for each geometric sequence. See Example 2.
- ,
12. , , 13. , 14.8, ,
Evaluate the indicated term for each geometric sequence. See Example 3.- , ; 16. , ; 17. , , ,Á; a 12
1
18
1
6
1
2
a 1 = 2 r= 5 a 10 a 1 = 1 r= 3 a 15Á
1
2
Á -2,
2
5
- Á 10, -2,
3
4
3
2
- 3,
- Á
2
9
- 2,
2
3
- 5,-10,-20,Á -2, -6, -18,Á ,
- Á
2
375
2
75
-
2
15
2
3
- Á
1
8
1
4
-
1
2
Á -3, -27, Á -8, -128,Á
11
7
8
7
5
7
Á
4
3
3
3
2
3
1
3
Á Á
- , , , ; 19. , ;a 7 = a 25 20.a 5 = 48 , ;a 8 =- 384 a 10
1
32
a 3 =1
2
Á a 181
6
1
3
2
3
Write the first five terms of each geometric sequence. See Example 4.- , 22. , 23. , 24. ,
Use the formula for to determine the sum of the terms of each geometric sequence. See Ex-
amples 5 and 6.In Exercises 27–32, give the answer to the nearest thousandth.- , , , , 26. , , , , ,
27. , , , , , 28. , , , ,
29. 30.
31. 32.
Solve each problem involving an ordinary annuity. See Example 7.
33.A father opened a savings account for his
daughter on her first birthday, depositing
$1000. Each year on her birthday he deposits
another $1000, making the last deposit on
her 21st birthday. If the account pays 4.4%
interest compounded annually, how much is
in the account at the end of the day on the
daughter’s 21st birthday?a^6i= 11 - 2 2a-1
2
bi
a10i= 11 -^2 2a3
5
bia8i= 15 a2
3
bi
a7i= 14 a2
5
bi5
256
-
5
128
5
64
-
5
32
5
16
-
4
729
-
4
243
-
4
81
-
4
27
-
4
9
-
4
3
128
3
64
3
32
3
16
3
8
3
4
3
1
243
1
81
1
27
1
9
1
3
Snr=-1
3
r=- a 1 = 61
5
a 1 = 2 r= 3 a 1 = 4 r= 2 a 1 = 5