Unit 5 Review
Sequences and Series
Fill out the following table for Sequence and Series formulas
Sequences
Recursive
Series
Infinite
Finite
Geometric
Arithmetic
Explicit
Name: _________________________
Find the first five terms of each sequence:
1. 𝐴𝑛 = 𝑛2 + 2𝑛
1
2. 𝐴𝑛 = 𝑛 − 6
3. 𝐴𝑛 = − 2 𝑛
Find the 100th term of each sequence (Hint: Use your explicit formula):
4. 10, 9, 8, 7, 6, …
5. 2, 4, 8, 16, …
Determine whether each sequence is arithmetic or geometric. Then, evaluate the finite series.
6. 1 + 3 + 9 + … n = 8
7. 25 + 32 + 39 + … n = 12
8. 13, 19, 25, 31
9. 16, 24, 36, 54
4
5
10. 20 + 4 + +
4
25
+…;n=6
11. 6 + (-18) + 54 + (-162) + …; n = 8
Determine whether each sequence is arithmetic, geometric, or neither. Then find the ninth term. (Hint: Write an
explicit formula)
12. 3, 12, 48, 192, …
13. -2, -7, -12, -17
2 2
14. 10, 2, 5, 25, …
1
7
15. 2, 2, 2, 5
Find the missing term of each arithmetic sequence.
16. 4,
, 24, 34, …
17. 100,
18. … , 2, ___, -14, …
, 92, …
Find the eighth term of each geometric sequence (Hint: Use your explicit formula):
19. 4, 8, 16
20. 20,480; 5,120; 1,280
Evaluate each infinite geometric series. (Hint: check divergence and convergence first)
21. ∑∞
𝑛=1(
−1 𝑛−1
)
2
24. 30 + 22.5 + 16.875 + …
27. 4 – 2 + 1 -
1
2
𝑛−1
22. ∑∞
𝑛=1 3(. 4)
23. 6, 18, 54, 162, …
25. 15 – 3 + .6 - .12 + …
26.
28. 5, -1, .2, -.04
5
2
12 + 6 + 3 + ….
5
4
29. -5 – - - …
Write a recursive definition for each sequence.
30. 80, 40, 20, 10
31. 4, 10, 16, 22
32. 3, 21, 147, 1029
Write a recursive and explicit formula for each sequence. Then find 𝑨𝟏𝟎 .
33. 41, 46, 51, 56, …
34. 1, 10, 100, 1000, …
35. 3, 6, 12, 24, 48
Find the missing term of each geometric sequence.
36. 16, ___, 4
37. 25, ___, 225
39. 1, ___, 49
40. 4, ___, 3
38. 2, ___, 50
3
41. 36, ___, 4
Find the sum of each finite series.
42. ∑5𝑛=1(𝑛 − 1)
43. ∑8𝑛=1 3𝑛
44. ∑15
𝑛=1(3𝑛 + 1)
45. ∑20
𝑛=1(5 − 𝑛)
Find the sum of each finite arithmetic series. (You will have to apply two formulas to get the answer)
46. 3 + 6 + 9 + … + 72
47. 6 + 12 + 18 + … + 108
48. (-2) + (-7) + (-12) + … + (-102)
Write each arithmetic series in summation notation. (∑
49. 1 + 5 + 9 + ... + 85
)
50. 5 + 11 + 17 + … + 371
51. 212 + 204 + 196 + … + (-20)
Find the sum of each finite geometric series. (You will have to apply two formulas to get the answer)
52. 5 + 15 + 45 + … + 10935
53.
1
6
1
Write an explicit formula for each arithmetic sequence. Then find the 12th term.
54. 2, 4, 6, 8, …
Find the 18th term of each arithmetic sequence.
55. 4, 1, -2, -5, …
1
+ 12 + 24 + … +
1
384
56. You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the
first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. What is the total
distance the object will fall in 6 seconds?
57. You complain that the hot tub in your hotel suite is not hot enough. The hotel tells you that they will increase the
temperature by 10% each hour. If the current temperature of the hot tub is 75º F, what will be the temperature of the hot
tub after 3 hours, to the nearest tenth of a degree?
58. A seashell has chambers that are each 0.82 times the length of the enclosing chamber. The outer chamber is 32 mm
around. Find the total length of the shell’s spiraled chambers.
59. Teddy gets better and better at a video game every time he plays. He scores 20 points in the first game, 25, in the
second, and 30 in the third and so on. How many points will he score the 15th time he plays?
60. Cami makes gift baskets for Easter. She has 13 baskets left over from last year, and she plans to make 12 more each
day. If there are 15 work days until the day she begins to sell the baskets, how many baskets will she have to sell?
61. Find the next three terms: f(2), f(3), and f(4). f(1) = 7
𝑓(𝑥) =
1
𝑓(𝑥
2
− 1) − 3
62. Given the arithmetic sequence: 3, 7, 11, …
what would the total be after 𝐴8