Sequence and Series Test Review
NAME: __________________________
Find the next four terms of each sequence.
1 2 3 4
1) , , , ,...
2 3 4 5
Find the first four terms of each sequence.
1
3) an  n 
n
2) 1,8, 27,64,...
4) an   1  22 n 
n
Find the indicated sum for each sequence. Show work.
5) Find the 4th partial sum of 𝑎𝑛 = 𝑎𝑛−1 + 3 where 𝑎1 = −2
6) Find S6 , given an 
n  n  1
2
Find each sum. Show work.
7
7)
  4n  7 
n 3
2
8)  4n 1
n 2
Determine the common difference, and find the next four terms of each arithmetic
sequence.
9) 17, 21, 25, 29,…
10) 15, 7, -1, -9,…
Find an explicit formula AND a recursive formula for the nth term of each arithmetic
sequence
11) 8, 6, 4, 2,…
12) 30, 26, 22, 18,…
Find the specified value for the arithmetic sequence with the given characteristics.
13) Find n, if 𝑎1 = 18, 𝑎𝑛 = 336 and d = 6.
14) If 𝑎20 = 61 and d = 4 find 𝑎1 .
Find the indicated sum of each arithmetic series.
15) 25th partial sum of 11 + 14 + 17 + 20 + …
16) 3 + 7 + 11 + … + 99
17) ∑45
𝑛=1 5 − 7𝑛
25 3𝑛
18)∑𝑛=1 2 − 1
Write each arithmetic series in sigma notation. The lower bound is given.
19) 1, 4, 7, 10,… ; n = 1
20) 23, 17, 11, 5,…; n = 1
Determine the common ratio, and find the next three terms.
21) 4, 8, 16, 32, …
22) 27, -18, 12, -8, …
Sequence and Series Test Review
Write an explicit formula AND a recursive formula for finding the nth term of each
geometric sequence.
23) 8, 4, 2, 1, …
24) 5, 10, 20, 40,…
Find the specified term for each geometric sequence or sequence with the given
characteristics.
2
25) Find 𝑎7 if 𝑎4 = 24 and r = 3
26) 𝑎7 for 64, -32, 16, -8, …
Find the indicated sum of each geometric series.
8
1
27) first n terms if 𝑎1 = 24, 𝑎𝑛 = , 𝑟 =
81
3
28) first eight terms of 0.3, 0.9, 2.7, 8.1, …
𝑛−1
29) ∑20
𝑛=1 3(2)
Determine if each infinite geometric series converges or diverges then, if possible, find the
sum.
1
30) 12−14+18−13
+⋯
31) -2 + 4 + -8 +16 + …
Find the missing quantity for the geometric sequence with the given characteristics.
32) Find n, if S = 511 and 1 + 2 + 4 +… + 256
33)Find 𝑎1 if 𝑆3 = −60 and r = 0.4
Write each geometric series in sigma notation.
34) 5 + 15 + 45 + … + 3645
1
1
1
35) 2 + 2 + 8 + ⋯ + 2048
Simplify, showing work.
36)
9!
3!7!
37)
12!
4!8!
Expand using Pascal’s triangle. Do NOT multiply out!
38)  x  y 
4
39)  2 x  4 y 
5
40) Find the coefficient of the 4th term in the expansion of  4x  y 
10
41) Find the coefficient of the a 6b5 term in the expansion of  3x  2 y 
11