Series and Sequences Practice Test
[Pages:4]Algebra 2
Name___________________________________
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Series and Sequences Practice Test
Date________________ Period____
Find the first four terms in each sequence.
1) a = n2 + 3 n
2n + 1 2) a =
n 2n
3) a = a ? -6
n
n - 1
a = -2 1
Evaluate each series.
7
S 5) (20 - k) k = 1
2 + a
4) a =
n - 1
n
2
a = -30 1
25
S 6) m2 m = 1
13
S 7) a a = 1
7
S 8) (2k2 - 2) k = 1
Determine if the sequence is arithmetic. If it is, find the common difference and the 52nd term.
9) -9, -16, -23, -30, ...
10) 30, 35, 40, 45, ...
Given two terms in an arithmetic sequence find the common difference and the term named in the problem.
11) a = -1038 and a = -3738
11
38
Find a 35
12) a = 27 and a = 111
10
31
Find a 38
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Worksheet by Kuta Software LLC
Evaluate each arithmetic series described. 13) 6 + 12 + 18 + 24..., n = 12
13
S 15) (3n - 4) n = 1
14) 16 + 19 + 22 + 25..., n = 15
40
S 16) (5n + 1) n = 1
Determine if the sequence is geometric. If it is, find the common ratio and the term named in the problem.
17) 2, 4, 8, 16, ... Find a
9
18) -4, 12, -36, 108, ... Find a
12
Given two terms in a geometric sequence find the term named in the problem.
19) a = 16 and a = 1024
2
5
Find a 9
20) a = 243 and a = 81
5
4
Find a 9
Evaluate each geometric series described. 21) 108 + 36 + 12 + 4..., n = 7
22) -1 - 3 - 9 - 27..., n = 8
S ( )9 1 i - 1
23) i=1 2
10
S 24) -2 ? 2n - 1 n = 1
Determine if the series converges or diverges. If it converges, evaluate the series described.
?
S 25) 4k - 1 k = 1
?
S 26) 2.7 ? 0.6m - 1 m = 1
S ( )? 4 k - 1
27) k=1 5
?
S 28) 1.8 ? 0.4m - 1 m = 1
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Worksheet by Kuta Software LLC
Algebra 2
Name___________________________________
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Series and Sequences Practice Test
Date________________ Period____
Find the first four terms in each sequence.
1) a = n2 + 3 n 4, 7, 12, 19
3) a = a ? -6
n
n - 1
a = -2 1
-2, 12, -72, 432
2n + 1 2) a =
n 2n
3579 , , ,
2468
2 + a
4) a =
n - 1
n
2
a = -30 1
-30, -14, -6, -2
Evaluate each series.
7
S 5) (20 - k) k = 1
112
25
S 6) m2 m = 1
5525
13
S 7) a a = 1
91
7
S 8) (2k2 - 2) k = 1
266
Determine if the sequence is arithmetic. If it is, find the common difference and the 52nd term.
9) -9, -16, -23, -30, ...
10) 30, 35, 40, 45, ...
Common Difference: d = -7 a = -366
52
Common Difference: d = 5 a = 285
52
Given two terms in an arithmetic sequence find the common difference and the term named in the problem.
11) a = -1038 and a = -3738
11
38
Find a 35
Common Difference: d = -100 a = -3438
35
12) a = 27 and a = 111
10
31
Find a 38
Common Difference: d = 4 a = 139
38
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Worksheet by Kuta Software LLC
Evaluate each arithmetic series described. 13) 6 + 12 + 18 + 24..., n = 12
468
13
S 15) (3n - 4) n = 1 221
14) 16 + 19 + 22 + 25..., n = 15 555
40
S 16) (5n + 1) n = 1 4140
Determine if the sequence is geometric. If it is, find the common ratio and the term named in the problem.
17) 2, 4, 8, 16, ...
18) -4, 12, -36, 108, ...
Find a 9
Find a 12
Common Ratio: r = 2
Common Ratio: r = -3
a = 512 9
a = 708588 12
Given two terms in a geometric sequence find the term named in the problem.
19) a = 16 and a = 1024
2
5
Find a 9
a = 262144 9
20) a = 243 and a = 81
5
4
Find a 9
a = 19683 9
Evaluate each geometric series described. 21) 108 + 36 + 12 + 4..., n = 7
4372 27
22) -1 - 3 - 9 - 27..., n = 8 -3280
S ( )9 1 i - 1
23) i=1 2
511 256
10
S 24) -2 ? 2n - 1 n = 1
-2046
Determine if the series converges or diverges. If it converges, evaluate the series described.
?
S 25) 4k - 1 k = 1
No sum
?
S 26) 2.7 ? 0.6m - 1 m = 1
6.75
S ( )? 4 k - 1
27) k=1 5
?
S 28) 1.8 ? 0.4m - 1 m = 1
5
3
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Worksheet by Kuta Software LLC
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