Algebra 2 - Sequences and Series Practice Test
Algebra 2
ID: 1
Name___________________________________
Sequences and Series Practice Test
Date________________ Period____
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Determine if the sequence is arithmetic. If it is, find the common difference.
1) -23, -31, -39, -47, ...
2) -23, -32, -41, -50, ...
3) 14, 7, 0, -7, ...
4) 21, 12, 3, -6, ...
Find the three terms in the sequence after the last one given.
5) -34, -134, -234, -334, ...
6) -21, -16, -11, -6, ...
Find the explicit formula. 7) -22, -222, -422, -622, ...
8) 35, 31, 27, 23, ...
Find the recursive formula. 9) 10, 8, 6, 4, ...
10) 23, 223, 423, 623, ...
Find the term named in the problem.
11) -39, -49, -59, -69, ... Find a
40
12) -27, -57, -87, -117, ... Find a
40
13) -14, -10, -6, -2, ... Find a
34
14) -2, -32, -62, -92, ... Find a
25
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-1-
Worksheet by Kuta Software LLC
Find the missing term or terms in each arithmetic sequence.
15) ..., 37, ___, -163, ...
16) ..., 36, ___, 96, ...
Determine if the sequence is geometric. If it is, find the common ratio.
17) -4, 12, -36, 108, ...
18) -1, 4, -16, 64, ...
19) -1, -5, -25, -125, ...
20) -1, 6, -36, 216, ...
Find the three terms in the sequence after the last one given.
21) 2, -12, 72, -432, ...
22) -4, -20, -100, -500, ...
Find the recursive formula. 23) -1, -6, -36, -216, ...
24) 2, 12, 72, 432, ...
Find the explicit formula. 25) 4, 8, 16, 32, ...
26) -2, -6, -18, -54, ...
Find the term named in the problem.
27) 4, 8, 16, 32, ... Find a
11
28) 1, 5, 25, 125, ... Find a
9
29) -1, -3, -9, -27, ... Find a
9
30) 4, -12, 36, -108, ... Find a
10
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-2-
Worksheet by Kuta Software LLC
Evaluate each arithmetic series described.
31) a = 14, a = 188, n = 30
1
n
32) a = 10, a = 66, n = 15
1
n
10
33) (2i + 6)
i = 1
12
34) (4 - 10i)
i = 1
Evaluate each geometric series described.
7
35) 2 (-5)n - 1
n = 1
8
36) 5n - 1
n = 1
37) a = 1, a = 15625, r = 5
1
7
38) a = 1, a = -2187, r = -3
1
8
Determine if each geometric series converges or diverges.
39) -0.9 - 0.18 - 0.036 - 0.0072...
40) -3 + 12 - 48 + 192...
41) 2 3k - 1
k = 1
( ) 125 4 n - 1
42) - n = 1 64 5
Evaluate each infinite geometric series described.
( )
1 k-1
43) -
k=1 2
( ) 3 1 i - 1
44) - i=1 2 5
11 2 4 45) - + - + ...
6 9 27 81
46) 32 + 16 + 8 + 4...
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-3-
Worksheet by Kuta Software LLC
Answers to Sequences and Series Practice Test (ID: 1)
1) d = -8
2) d = -9
3) d = -7
4) d = -9
5) -434, -534, -634
9) a = a - 2 n n-1 a = 10 1
13) a = 118 34
17) r = -3
6) -1, 4, 9
10) a = a + 200 n n-1 a = 23 1
14) a = -722 25
18) r = -4
7) a = 178 - 200n n
11) a = -429 40
15) -63 19) r = 5
8) a = 39 - 4n n
12) a = -1197 40
16) 66 20) r = -6
21) 2592, -15552, 93312
22) -2500, -12500, -62500
23) a = a 6 n n-1
a = -1
1
24) a = a 6 n n-1
a =2
1
25) a = 4 2n - 1 n
26) a = -2 3n - 1 n
27) a = 4096 11
28) a = 390625 9
29) a = -6561 9
30) a = -78732 10
31) 3030
32) 570
33) 170
34) -732
35) 26042
36) 97656
37) 19531
38) -1640
39) Converges
40) Diverges
41) Diverges
42) Converges
2 43)
3
15 44) -
8
1 45) -
10
46) 64
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-4-
Worksheet by Kuta Software LLC
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