Honors Algebra 2
Name___________________________________
Sequences and Series
Date________________ Period____
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Determine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, the term
named in the problem, and the explicit formula.
1) 1, 9, 25, 49, ...
Find a30
2) 2, 4, 12, 48, ...
Find a26
Given the explicit formula for an arithmetic sequence find the common difference, the 52nd term, and the
term named in the problem.
3) an = 36 + (n − 1) ⋅ 20
4) an = 12 + (n − 1) ⋅ −10
Find a28
Find a27
Given two terms in an arithmetic sequence find the common difference, the 52nd term, and the term named
in the problem.
5) a11 = 35 and a39 = 203
6) a11 = −81 and a31 = −241
Find a28
Find a39
Given the first term and the common difference of an arithmetic sequence find the 52nd term and the term
named in the problem.
7) a1 = −6, d = 7
8) a1 = 19, d = −30
Find a40
Find a39
Given a term in an arithmetic sequence and the common difference find the 52nd term and the term named
in the problem.
9) a26 = 4982, d = 200
10) a35 = 177, d = 5
Find a34
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Find a30
-1-
Worksheet by Kuta Software LLC
Find the missing term or terms in each arithmetic sequence.
11) ..., −15, ___, ___, ___, ___, ___, −75, ...
12) ..., −32, ___, ___, ___, ___, 13, ...
13) ..., 30, ___, ___, ___, 22, ...
Find the missing term or terms in each geometric sequence.
14) ..., 2, ___, ___, ___, ___, ___, 128, ...
15) ..., 4, ___, ___, ___, 64, ...
16) ..., −4, ___, ___, ___, ___, −972, ...
Evaluate the related series of each sequence.
17) 25, 32, 39, 46, 53, 60, 67
18) 22, 26, 30, 34
Evaluate each arithmetic series described.
15
19)
21)
Σ (8m − 7)
7
20)
Σ (7i − 4)
m=1
i=1
35
50
Σ (15 − 9i)
22)
i=1
23) a1 = 5, an = 19, n = 8
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Σ (5 − 9n)
n=1
24) a1 = 10, d = 4, n = 6
-2-
Worksheet by Kuta Software LLC
25) a1 = 17, d = 4, n = 20
26) (−1) + 8 + 17 + 26..., n = 8
Determine the number of terms n in each arithmetic series.
27) a1 = 8, an = 50, S n = 435
28) a1 = 23, an = 137, S n = 1600
Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit
formula.
29) −3, 12, −48, 192, ...
30) −4, 16, −64, 256, ...
Given the explicit formula for a geometric sequence find the common ratio and the 8th term.
31) an = −4 ⋅ (−2)
n−1
32) an = 2 ⋅ (−6)
n−1
Given two terms in a geometric sequence find the common ratio and the 8th term.
33) a3 = 16 and a4 = 32
34) a3 = 16 and a4 = −32
Given the first term and the common ratio of a geometric sequence find the 8th term.
35) a1 = −2, r = 3
36) a1 = −2, r = 4
Given the second term and the common ratio of a geometric sequence find the 8th term and the term named
in the problem.
37) a2 = −6, r = −2
38) a2 = 6, r = 2
Find a9
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Find a10
-3-
Worksheet by Kuta Software LLC
Given a term in a geometric sequence and the common ratio find the 8th term and the term named in the
problem.
39) a2 = 3, r = −3
40) a4 = 27, r = 3
Find a9
Find a12
Given two terms in a geometric sequence find the 8th term and the term named in the problem.
41) a5 = −16 and a1 = −1
42) a1 = 3 and a3 = 12
Find a10
Find a12
Evaluate each geometric series described.
43) 2 + 10 + 50 + 250..., n = 9
10
44)
Σ4
n−1
n=1
7
45)
Σ
2 ⋅ 5k − 1
46) a1 = −3, an = −6561, r = 3
k=1
47) a1 = −1, a8 = −16384, r = 4
48) −2 − 8 − 32 − 128..., n = 9
Determine the number of terms n in each geometric series.
49) a1 = −2, r = 3, S n = −26
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50) a1 = −2, r = 3, S n = −728
-4-
Worksheet by Kuta Software LLC
Answers to Sequences and Series
1) Not arithmetic
2) Not arithmetic
3) Common Difference: d = 20
a52 = 1056
a28 = 576
4) Common Difference: d = −10
a52 = −498
a27 = −248
5) Common Difference: d = 6
a52 = 281
a28 = 137
7) a52 = 351
8) a52 = −1511
a40 = 267
a39 = −1121
11)
14)
17)
21)
25)
29)
−25, −35, −45, −55, −65
4, 8, 16, 32, 64
15)
322
18)
−5145
22)
1100
26)
Common Ratio: r = −4
a8 = 49152
35) a8 = −4374
a39 = −305
9) a52 = 10182
a34 = 6582
a9 = −6561
43) 976562
47) −21845
a30 = 152
Explicit: an = −4 ⋅ (−4) n − 1
33) Common Ratio: r = 2
a8 = 512
36) a8 = −32768
37) a8 = −384
a9 = 768
39) a8 = 2187
10) a52 = 262
12) −23, −14, −5, 4
13) 28, 26, 24
8, 16, 32
16) −12, −36, −108, −324
112
19) 855
20) 168
−11225
23) 96
24) 120
244
27) 15
28) 20
30) Common Ratio: r = −4
31) Common Ratio: r = −2
a8 = 65536
a8 = 512
Explicit: an = −3 ⋅ (−4) n − 1
32) Common Ratio: r = −6
a8 = −559872
6) Common Difference: d = −8
a52 = −409
40) a8 = 2187
41) a8 = 128
a12 = 177147
44) 349525
48) −174762
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a10 = 512
45) 39062
49) 3
-5-
34) Common Ratio: r = −2
a8 = −512
38) a8 = 384
a10 = 1536
42) a8 = 384
a12 = 6144
46) −9840
50) 6
Worksheet by Kuta Software LLC