Problem Set 9.1
For Problems 1-10, write the first five terms of the sequence that has the indicated general term. .
I. an
= 3n - 7
--4, -1,2,5,8
• an = -2n
+4
2,0, -2, -4, -6
• an
=
3n2
-
1
2, 11,26,47, 74
2. an = 5n - 2
3,8, 13, 18,23
4. an
=
-4n + 7
3, -1, -51 -9, -13
= 2n2 -\6
-4, 2, 12, 26, 44
6. an
7. an = n(n - 1)
0,2,6,12,20
= 2n+1
4,8,16,32,64
9. an
ill.
8. an = (n
+
l)(n
+ 2)
6,12,20,30,42
iLO. an
= 3n -
1
1,3,9,27,81
Find the 15th and 30th terms of the sequence where
4. - a,s = -79; a30 = -154
an = -5n -
U.
Find the 20th and 50th terms of the sequence where
an = -n - 3.
a20 = ~23;
aSO= -53
~S'. Find the sum of the first 50 terms of the arithmetic
sequence 5, 7,9,11,13, . . . . 2700
[iJ.
Find the 25th and 50th terms of the sequence where
an=(-l)n+l.
a2s=1;
aso=-1
36. Find the sum of the first 30 terms of the arithmetic
l~.Find the 10th and 15th terms of the sequence where
37. Find the sum of the first 40 terms of the arithmetic
an
=
-n2
-
10.
alO = -110;
an
=
16.7,10,13,16,19, ...
2n + 9
an
[7;. 2, -1, -4, -7, -10, ...
an
+4
+ 5
= 3n
= -3n
~. Find the sum of the first 75 terms of the arithmetic
sequence 5, 2, -1, -4, -7, . . . . -7950
40. Find the sum of the first 80 terms of the arithmetic
sequence 7, 3, -1, -5, -9,....
'"
an =
3200
~. Find the sum of the first 60 terms of the arithmetic
sequence -2,3,8,13,18, . . . . 8730
OCB:. 4,2,0, -2, -;-4,...
,.-,3
5
7
112. 2,2, 2,3, 2'"
870
sequence 2, 6, 10, 14, 18, . . . .
a,s = -235
For Problems 15-24, find the general term (the nth term)
for each arithmetic sequence.
~. 11,13,15,17,19, ...
sequence 0, 2, 4, 6, 8, . . . .
1
3
41. Find the sum of the first 50 terms of the arithmetic
20. 0, 2' 1, 2,2, ...
.
1
3
5
sequence 2,1, 2' 2, 2'"
an=Y
n ~ 2
21. 2,6,10,14,18, ...
22.2,7,12,17,22, ...
an = 4n - 2
an = 5n - 3
23. -3, -6, -9, -12, -15, ...
an = -3n
-12,080
..
~~ Find the sum of the first 100 terms of the arithmetic
1 1
5 7
sequence -3' 3,1, 3' 3" ...
3266.6
For Problems 43-50, find the indicated sum.
For Problems 25-30, find the required term for each arithmetic sequence.
~. 1 + 5 + 9 + 13 + ' .. + 197
2 ~ The 15th term of 3, 8, 13, 18, . . .
44. 3 + 8 + 13 + 18 + ... + 398
16,040
~. 2+8+14+20+"'+146
1850
26. The 20th term of 4, 11, 18, 25, . . .
73
137
~~. The 30th term of 15,26,37,48, . . .
334
46. 6 + 9 + 12 + 15 + ... + 93
4950
1485
28. The 35th term of 9,17,25,33, ...
~. (-7) + (-10) + (-13) + (-16) + ... + (-109)
,---,
48. (-5) + (-9) + (-13) +'(-17)
-2030
5 7
~~. The 52nd term of 1, 3' 3' 3, ...
+ ... + (-169)
-3654
"'"'"
15
11
~. The 47th term of2, 4' 2'4""
For Problems 31-42, solve each problem.
~
32. If the 5th term of an arithmetic sequence is 14 and the
M.
~. (-7) + (-4) + (-1) + 2 + .. , + 131
2914
~. Find the sum of the first 200 odd whole numbers.
40,000
52. Find the sum of the first 175 positive even whole
numbers.
-2
33. If the 3rd term of an arithmetic sequence is 20 and the
7th ,term is 32, find the 25th term.
3591
For Problems 51-58, solve each problem.
If the 6th term of an arithmetic sequence is 12 and the
10th term is 16, find the first term.
7
12th term is 42, find the first term.
49. (-5)+(-3)+(-1)+1+"'+119
53. Find the sum of all even numbers between 18 and 482,
inclusive.
86
If the 5th term of an arithmetic sequence is - 5 and the
15th term is -25, find the 50th term.
-95
30,800
S4.
58,250
Find the sum of all odd numbers between 17 and 379,
inclusive. 36,036
55. Find the sum of the first 30 terms of the arithmetic
sequence with the general term an
=
5n - 4.
2205
=
4n - 7.
3000
Arithmetic
-810
62.
+
4)
i=1
L(3i
sequence with the general term an = -4n - l.
1276
64.
-1325
L4i
of the first 35 terms of the arithmetic
sequence with the general term an = -5n - 3.
-3255
LF
45
59.
L (5i
i=1
38
+ 2)
5265
60.
L (3i
i=l
"
+
6)
2451
4074
L (-5i)
-1800
L (F + 1)
97
1=1
8
L (2F + i)
i~3
- 9)
6
68.
55
i=1
69.
L(4i
i~15
5
67.
-2340
30
66.
660
i~10
58. Find the sum
+ 3)
i=6
20
65.
L (-3i
47
- 10)
i=4
57. Find the sum of the first 25 terms of the arithmetic
651
i=1
32
63.
Sequences
40
30
!il. L(-2i
56. Find the sum of the first 40 terms of the arithmetic
sequence with the general term an
9.1
7
431
70.
L(3F-2)
i~4
370
Problem Set 9.2
For Problems 1-12, find the general term (the nth term) for
each geometric sequence.
l!. 3, 6, 12,24, ...
2. 2, 6, 18, 54, ...
an = 2(3)"-1
an = 3(2)"-'
3. 3,9,27,81,
...
an
=
3n
4. 2,4,8,16,
...
an
= 2n
1. 1, -2,4, -8, ...
u. -3,9, -27,81, ...
an = (_2)"-1
For Problems 13-20, find the required term for each geometric sequence.
1
113. The 8th term of "2' 1, 2, 4, . . .
1 1 1 1
5.4'8' 16' 32""
an = (~)n+'
2 2
8. 6,2,
3' 9""
an = 6(~)"-'
an = (-3)n
64
~. The 8th term of -1,
\i2.
3
-2'
9
4'
27
8""
1 1 1 1
The 8th term of 2' 6"' 18' 54' ...
2187
128
1
4374
16 8 4 2
20. The 9th term of 81 ' 27 ' 9" 3 ' ...
B • 4
+2 +
1
+ .. - +
1
512
511
7
512
l36'.1 + (-2) + 4 + ... + 256
B
I.
171
(-1) + 3 + (-9) + ... + (-729)
1
68. 16 + 8 + 4 + ... + 32
-547
31
32
31
For Problems 21-32, solve each problem.
~. Find the first term of the geometric sequence with
5th term
32
d
3
an common
.'
ratlO 2.
2
9
6
6. 2:2i-3
i~1
3"
'10. 2:3;
i~1
127~
4
5
~~. Find the first term of the geome-tric sequence with
27
. 3
1
4th term 128 and common raho 4'
"2
I"j. Find the common ratio of the geometric sequence with
3rd term 12 and 6th term 96. 2
124.Find the common ratio of the geometric sequence
.
8
64
~]i.
8
L (-3y+1
42.
540
i=2
43.
6
i~3
L (-2y-1
CY2
2~
64
5
~23
CY
46. 9,3,1,
25. Find the sum of the first ten terms of the geometric
sequence 1, 2, 4, 8, . . . . 1023
1
'3' ...
9 27
48. 5, 3,5" 25' ...
!:t9. 4, 8, 16, 32, ...
1
27. Find the sum of the first nine terms of the geometric
sequence 2, 6,18,54, . . . . 19,682
242
243
-
For Problems 45-56, find the sum of each infinite geometric sequence. If the sequence has no sum, so state.
2
Find the sum of the first seven terms of the geometric
sequence 3, 9, 27, 81, . . . . 3279
-84
i=3
3"
wIth 2nd term 3 and 5th term 81'
!26.
1092
511.9, -3, 1, -3"
3
No sum
..
27
'4
.!.~~~
50. 32,16,8,4,...
2. 2, -6,18,
54. 4,
-54, ...
64
Nosum
4 4
4
3 ' 9' - 27' . . .
28. Find the sum of the first ten terms of the geometric
sequence 5, 10, 20, 40, . . . . 5115
5 . 2' 8' 32' 128' . ..
~. Find the sum of the first eight terms of the geometric
sequence 8,12,18,27, . . . . 394t,;
55. 8, -4,2, -1, ...
30. Find the sum of the first eight terms of the geomet-
For Problems 57-68, change each repeating decimal to a/b
form, where a and b are integers and b O. Express a/b in
reduced form.
.
nc sequence 9,12,16,
64
169
242
243
3' ....
Ml. Find the sum of the first ten terms of the geometric
sequence -4,8, -16,32, . . . .
1364
32. Find the sum of the first nine terms of the geometric
sequence - 2, 6, -18,54, . . . .
-9842
57.
0.3
34. 2 + 8 + 32 +
+ 729
+ 8192
1089
10,922
~
26
59. 0.26
-
99
41
61. 0.123
333
4
15
65. 0.214
67. 2.3
-
495
7
3
60. 0.18
6 '. 0.273
64. 0.43
106
3
14 28 56
r~6
7--,.,. '5' 25' 125' ...
*
63. 0.26
§J. 9 + 27 + 81 +
2
66. 0.371
68: 3.7
2
11
91
333
13
30
184
495
34
9