Sequences/Series Test Practice Date Period
ID: 1
Algebra 2
Name___________________________________
Sequences/Series Test Practice
Date________________ Period____
If the sequence is arithmetic or geometric, find the next 3 terms.
5
5
5
5
, ...
1) ?5, ? , ? , ? , ?
4
16
64
256
2) 1, 3, 6, 10, 15, ...
3) ?11, 89, 189, 289, 389, ...
4) ?38, ?36, ?34, ?32, ?30, ...
Given the first term and the common difference of an arithmetic sequence find the term named in the
problem.
5) a1 = ?9, d = 2
6) a1 = ?14, d = ?10
Find a20
Find a38
Find the missing term or terms in each arithmetic sequence.
7) ..., ?20, ___, ___, ___, 0, ...
8) ..., 26, ___, ___, ___, ___, 41, ...
Given the first term and the common ratio of a geometric sequence find the term named in the problem.
9) a1 = ?4, r = ?2
10) a1 = 2, r = ?2
Find a10
Find a11
Find the missing term or terms in each geometric sequence.
11) ..., ?1, ___, ___, ___, ?256, ...
12) ..., ?2, ___, ___, ___, ___, ?2048, ...
Evaluate each arithmetic series described.
8
13)
¦² (2k + 7)
10
14)
k=2
¦² (5 ? 3i)
i=3
15) a1 = 16, d = 3, n = 5
16) a1 = 7, d = 7, n = 45
17) 6 + 8 + 10 + 12..., n = 7
18) (?2) + 2 + 6 + 10..., n = 19
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-1-
Worksheet by Kuta Software LLC
Determine the number of terms n in each arithmetic series.
19) a1 = 26, an = 166, S n = 1440
20) a1 = 10, an = 451, S n = 11525
Evaluate each geometric series described.
21) ?3 + 15 ? 75 + 375..., n = 6
9
23)
¦²
i=1
()
1
?2 ?
5
22) 1 + 5 + 25 + 125..., n = 8
7
i?1
24)
¦² 2 ? (?6)
i?1
i=1
Evaluate each infinite geometric series described.
¡Þ
( )
4
25)
108 ? ?
3
m=1
¦²
27) 6 ?
m?1
3 3
3
+ ? ...
2 8 32
¡Þ
()
1
26)
?2 ?
2
n=1
¦²
28) 2 ?
n?1
2 2
2
+ ? ...
3 9 27
Determine the number of terms n in each geometric series.
29) a1 = ?2, r = ?6, S n = 13330
30) a1 = ?3, r = ?6, S n = 555
Given the recursive formula for an arithmetic sequence find the first five terms.
31) an + 1 = an + n
32) an + 1 = an ? an + 1
a1 = 7
a1 = 2
a2 = 3
33) an + 1 = an + n
34) an + 1 = an + n
a1 = 3
a1 = ?10
35) an + 1 = an + n
36) an + 1 = an + 9
a1 = ?9
a1 = ?13
37) an + 1 = an ? 4
38) an + 1 = an ? ?5
a1 = ?2
?N VKnuWtXal 4SDojfdtkwKaKrZeC SLyLACI.z o xAHlAlm erWiFgHhIt6ss grleQsKe8rRv5eYdz.5 5 2MIacd1eN JwBiItMh2 rIJnFfUibnbiOtHez rAsltgke5bor2aC 42e.c
a1 = 3
-2-
Worksheet by Kuta Software LLC
Answers to Sequences/Series Test Practice (ID: 1)
2) 21, 28, 36
5
5
5
, ?
, ?
1024
4096
16384
4) ?28, ?26, ?24
5) a20 = 29
3) 489, 589, 689
6) a38 = ?384
8) 29, 32, 35, 38
10) a11 = 2048
1) ?
11)
14)
18)
22)
26)
30)
34)
37)
9) a10 = 2048
7) ?15, ?10, ?5
?4, ?16, ?64 or 4, -16, 64
12) ?8, ?32, ?128, ?512
13) 119
?116
15) 110
16) 7245
17) 84
646
19) 15
20) 50
21) 7812
25) No sum
97656
24) 79982
976562
23) ?
390625
?4
29) 6
24
3
27)
28)
5
2
32) 2, 3, -1, 4, -5
4
31) 7, 12, 17, 22, 27
33) 3, 5, 8, 12
?10, ?8, ?5, ?1
35) ?9, ?7, ?4, 0
36) ?13, ?4, 5, 14
?2, ?8, ?32, ?128, ?512
38) 3, ?15, 75, ?375, 1875
?x OKduet7ak pSXoAfStVw1aXreev pLjLGCM.3 s KAhlTl7 0rKiDgmhWtIsn RrlemseeyrfvheEdp.B o XM7agdZeb Ow2iQt2hJ CIQnpfLi0nEivtpeV sA2l7gxeZbMrnaJ b2C.Q
-3-
Worksheet by Kuta Software LLC
ID: 2
Algebra 2
Name___________________________________
Sequences/Series Test Practice
Date________________ Period____
If the sequence is arithmetic or geometric, find the next 3 terms.
1) 4, ?8, 16, ?32, 64, ...
3) 3, 15, 75, 375, 1875, ...
5 7 9 11
, ,
,
, ...
4 9 16 25
2) 3,
4) 1, 4, 9, 16, 25, ...
Given the first term and the common difference of an arithmetic sequence find the term named in the
problem.
5) a1 = 6, d = 2
6) a1 = ?39, d = ?3
Find a22
Find a39
Find the missing term or terms in each arithmetic sequence.
7) ..., 32, ___, ___, ___, 8, ...
8) ..., 1, ___, ___, ___, ___, 501, ...
Given the first term and the common ratio of a geometric sequence find the term named in the problem.
9) a1 = ?1, r = ?2
10) a1 = ?4, r = 3
Find a11
Find a11
Find the missing term or terms in each geometric sequence.
11) ..., 2, ___, ___, ___, ___, 15552, ...
12) ..., 3, ___, ___, ___, ___, 9375, ...
Evaluate each arithmetic series described.
10
13)
¦² (7k ? 12)
10
14)
k=3
¦² (8m ? 5)
m=5
15) a1 = ?10, d = ?10, n = 13
16) a1 = 6, d = ?2, n = 9
17) (?4) + (?2) + 0 + 2..., n = 8
18) 17 + 20 + 23 + 26..., n = 7
Determine the number of terms n in each arithmetic series.
19) a1 = 5, an = 65, S n = 455
?L 1KtuXtmas ySPoBfRt4wRaYrbeg ULvLGCk.N 0 HATlCly vrCiDghhFt0sn rrdeKswevrlv4eqd5.u b EM0avdze2 iwriEtZhD 4IFnLfxibnZibt9ee CARligZeYbfrdaa o2F.Q
20) a1 = 15, an = 35, S n = 150
-1-
Worksheet by Kuta Software LLC
Evaluate each geometric series described.
21) ?4 ? 24 ? 144 ? 864..., n = 6
22) ?
9
23)
¦²
1 1
1
1
+ ?
+ ..., n = 7
4 8 16 32
8
4
n?1
24)
n=1
¦²5
m?1
m=1
Evaluate each infinite geometric series described.
¡Þ
25)
¦²
m=1
27) 3 +
()
27 4
?
32 3
m?1
3
3
3
+
+ ...
4 16 64
¡Þ
26)
¦²
n=1
?
()
27 2
?
2
3
n?1
28) ?1.3 ? 1.04 ? 0.832 ? 0.6656...
Determine the number of terms n in each geometric series.
29) a1 = ?4, r = ?6, S n = ?124
30) a1 = ?1, r = 2, S n = ?7
Given the recursive formula for an arithmetic sequence find the first five terms.
31) an + 1 = an ? 7
32) an + 1 = an ? 2
a1 = ?40
a1 = 30
33) an + 1 =
2 + an
34) an + 1 = an + n
2
a1 = ?6
a1 = ?22
35) an + 1 = an ? 2
36) an + 1 = nan
a1 = 1
37) an + 1 = an ? ?4
a1 = ?1
38) an + 1 = an ? ?5
a1 = 1
?8 EKmuOtka8 7SQozfTtowwakrceI 9LVLLCt.2 e 3Abl2lk irKiYg4hetEse YrqeNs3eprSvQeGd9.R g AMoardneI lwgiPtehn cI7nXfXi8nniBteeF 7A5l3gCeHbHrsaf z2S.z
a1 = ?3
-2-
Worksheet by Kuta Software LLC
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