# Unit #12 Sequences and Series Review

```Unit #12 Sequences and Series Review
1) The sum of the arithmetic sequence 19+27+35+43+51 can be represented as which of the following?
5
a)
51
 11  8n 
b)
n 1
n 19
5
c)

 19 
n 1 

2 
1
 19  8n 
d)
n 0
 19  8n 
n 5
2) What is the sixth term of the geometric sequence defined as an  5(.4) n 1
a) 32
c) 0.1024
b) 0.0512
d) 0.02048
3) Which of the following formulas could be used to find the nth term of the following arithmetic sequence:
25,31,37,43 . . .
a)
an  19  6(n  1)
b) an  25  6n
c)
an  25  6(n  1)
d) an  25(6) n 1
4) In a geometric sequence, if a2  162 and a5  6 , what is the value of r?
1
2
1
c) 
3
a)
1
3
1
d)
2

5) Find the first five terms of each sequence.
a)
b) an1  an  3,
an  n 2  1
b)
a1  5
1
c)
an  2  an1   7, a1  2
6) Use a formula to find the sum of the following geometric sequence. Show your work.
6-12+24-48+96-192+384-768
7) Find the sum of the first 27 terms of an arithmetic sequence where the first term is 5 and the common
difference is 6. Write the formula you used.
a) Determine if the sequence arithmetic, geometric, or neither. If it is neither, do not do b) or c).
b) Depending on the type of sequence, find the common difference or ratio.
c) Find the 12th term of the sequence. Write the formula you used.
8)
-3,4,11,18 . . .
9)
144,-72,36,-18 . . .
10) 74,65,56,47 . . .
11) 4,12,36,108 . . .
2
12) Use sigma notation to write a rule for the sum of the first eight terms of the geometric series, 7+21+63+189 . . . .
13) Express the following sum using sigma notation: 5 + 9 + 13 + 17 + 21 + 25.
 2k  3 

k 
k 1
10
14) Use your calculator to evaluate the following sum:
 
15) Write an algebraic formula for each of the following sequences.
a) 3,5,7,9 . . .
b) 1,4,9,16,25 . . .
c) 4,16,64, 256 . . .
20
16) Write out the first three terms of the following series. Then use a formula to find the sum:
17) In your own words explain how to use the following recursive definition to find a2 and a3 .
an 1   an   6, a1  5
2
3
  4n  12 
n 1
18) Use a formula to find the sum of first 70 terms of the following arithmetic sequence. Show your work.
-20,-15,-10,-5, . . .
19) Find the 200th term of the following sequence: 6, 12, 18, 24 . . .
20) Find the sum of the first 10 terms of a geometric sequence where the first term is 2, the common ratio is -3.
3
(2m  1)
21) What is the value of 
m 1
m 1
?
1) 15
2) 55
3) 57
4) 245
5
22) Find the value of the following expression by hand:
2 (  n 2  2 n )
n 0
 What buttons should you use to check your answer using the calculator?
4
```