Review
Arithmetic and Geometric
Series and Sequences
NAME __________________________
DATE__________________________
1. Write the first five terms of the arithmetic sequence. 𝑎𝑛 = 3𝑛 + 5.
2. Find the 11th term of the sequence. 𝑎𝑛 = (−1)𝑛 (2𝑛 − 4).
3. Write an expression for the nth term of the sequence. -12, -6, 0, 6, 12…
4. Find the sum of the sequence 13, 8, 3, -2, -7…, when we have 15 terms.
5. Find three arithmetic means between 1 and 17.
6. Evaluate the arithmetic series.
3
∑𝑛+9
𝑛=1
7. Rewrite the series using sigma notation. 2 + 4 + 6 + 8.
8. Find three arithmetic means between 7 and 15.
9. Write an expression for the nth term of the sequence. 𝑎4 = 9, 𝑎7 = 24.
10. Find sum of the arithmetic sequence. 2.2, 3.3, 4.4, 5.5..., when we have 35 terms.
11. Several logs are stored in a pile with 12 logs on the bottom layer, 11 on the second layer, 10
on the third layer, and so on. If the top layer has one log, how many logs are in the pile?
12. Determine whether the sequence is geometric or arithmetic. If it is geometric find the
common ratio, if it is arithmetic find the common difference. 4, 12, 36, 108...
13. Write the first four terms of the geometric sequence. 𝑎1 = −2, 𝑟 = 4.
14. Find the 8th term of the geometric sequence.
1 1
, , 1, …
4 2
15. Evaluate the geometric sequence.
4
∑ −2(3)𝑛
𝑛=0
16. Find four geometric means between -1 and -243.
17. Evaluate the geometric series. 𝑎1 = −1, 𝑟 = −2 if you have 7 terms.
18. Find the sum of the infinite geometric sequence.
∞
1
∑ 5( )𝑛−1
5
𝑛=1
19. Find one geometric mean between 10 and 250.
20. Find the sum of the infinite geometric sequence. 12 + 6 + 3 + …