Pre-Calculus
Sequences and Series Unit Review Sheet
Name: _____________________________________
For numbers 1 – 3, decide whether the sequence is arithmetic, geometric, or neither. If it is arithmetic or geometric find the rule for
the nth term.
1 1 1 1
2. –1, –4, –7, –10, –13, …
3. 1, 2, 4, 8, 16, …
1. 1, , , , ,...
2 4 8 16
For numbers 4 and 5, write the terms of the series. Then evaluate the sum.
5
4.
7
∑ (n − 5)
5.
n =1
∑ (i − 1)
2
i =3
For numbers 6 and 7, evaluate the sum of the arithmetic series.
25
6.
40
∑ (4i )
7.
i =1
∑ (3i − 10)
i =1
For numbers 8 – 10, evaluate the sum of the finite or infinite geometric series. (The infinite geometric series problems may not have
a sum.)
12
8.
∑ (3)(2)n−1
n =1
∞
9.
3
∑ (− 1) 2 
n =1
n −1
10.
 
For numbers 11 and 12, write the first five terms of the following sequences.
11. a1 = 6, r =
1
2
12. a1 = 7, d = –12
13. Write a rule for the nth term of the arithmetic sequence: a5 = 18, a17 = 66
∞
 1  3 
n =1
  
∑  2  4 
n −1
14. Find a84 for the arithmetic sequence: 12, 6, 0, ….
15. Find S84 for the arithmetic series 12 + 6 + 0 + ….
16. Find n if Sn = –10,602 for the arithmetic series 12 + 6 + 0 + ….
For numbers 17 and 18, determine if the infinite series has a sum. Justify your response.
51
∑ 89
 
n =1
∞
17.
n −1
 8
∑ 7 − 7 

n =1 
∞
18.
19. Write the repeating decimal as a fraction: 0.5833
20. Find the sum of the first 15 terms of the geometric series: 5 – 15 + 45 – 135 + …
21. Use the series in #20 to find n when Sn = –8200
22. Write a rule for the nth term of the geometric sequence: a2 = 6, a5 = 162
n −1
23. In a geometric sequence, a2 = 64 and a5 = –8. Find a9.
24. In a arithmetic sequence a3 = 8 and a5 = 14. Find a50.
25. Consider the sequence of all multiples of 3 between 1 and 200.
b) Find the sum of the sequence.
a) Find the rule for an.
Numbers 26 – 32 are multiple choice.
26. Which of the following series converges?
a)
1 3 9 27
+ + +
+ ...
2 2 2 2
b) –40 – 20 – 10 – 5 – …
d) 100 – 110 + 121 – 133.1 + …
c) 10 + 15 + 22.5 + 33.75 + …
e) 50 + 100 + 200 + 400 + …
27. An infinite geometric series has a sum of 200 and a common ratio of 0.4. What is the first term of the series?
a) 80
b) 120
c) 333
d) 500
e) 650
d) 27
e) 32
28. What is S6 for the arithmetic series 4 + 4.2 + 4.4 + 4.6 + 4.8 + …?
a) 5
b) 15
c) 20
29. What is the common ratio of the geometric sequence
a)
1
3
b)
1
2
3 3
, , 3, 6 , ...?
4 2
c) 2
d)
30. What is the approximate sum of the geometric series ∑ 3(0.9 )
8
5
2
e) 3
m −1
m =1
a) 6
b) 9
c)
19
2
d) 12
e) 17
31. Which is summation notation for the series 2 + 4 + 8 + 16?
4
a)
∑ 2k
k =1
4
4
b)
∑2
k =0
k
c)
∑k
4
2
k =1
d)
∑ 2k
k =0
4
e)
∑2
k =1
32. What is the common difference of the sequence 3, 4.5, 6, 7.5, …?
a) 1.5
b) 2
c) 3
d) 4.5
e) 5
k