Sequences and Series – Practice Worksheet
1. What is the sum of the next two terms of the sequence: -3, -1, 3, 9, 17, …
66
2.
Write the first four terms of the sequence having the formula tn
3.
Identify each sequence as arithmetic, geometric, or neither.
a) 1, 2, 4, 7
b) 2, 3, 5, 7
c) 1, 2, 4, 8
neither
neither
geometric
 2 

n
8
the sequence is arithmetic, geometric, or neither. -1/4, ½, -1, 2  geometric
d) 1, 3, 9, 27
geometric
f) m, m2 , m3 , m4
geometric
e) 2, 4, 8, 12
neither
. Then tell whether
d) -3, 1, 5, 9
arithmetic
g) m, 2m,3m, 4m
arithmetic
What is the 9th term of the sequence 2a  b, a, b,... ?
-6a + 7b
1
5. What is the nth term of the geometric sequence ,1,3,... ?
3
an = 1/3 (3)n-1
4.
8
6. Evaluate
3 2
k 1
k 1
765
 m 1
?
m 
m2
7
7.
What is the 5th term in the expansion of
 
7/6
8. Write the arithmetic series 2 + 5 + 8 + … + 299 using summation notation.
100
 2  3(n  1)
n 1
9. Suppose on Jan. 1 you deposit $1.00 in an empty piggy bank. On Jan. 8 you deposit $1.50;
on Jan. 15 you deposit $2.00; and each week thereafter you deposit $0.50 more than the previous
week.
a) What kind of sequence do these deposits generate? arithmetic
b) What amount will you deposit in the 52nd week? $26.50
c) What is the total in the piggy bank at the end of these 52 weeks? $715.00
10. A snail is crawling straight up a wall. The first hour it climbs 16 inches, the second hour it
climbs 12 inches, and each succeeding hour, it climbs only three-fourths the distance it climbed
the previous hour. Assume the pattern continues.
a) How far does the snail climb during the seventh hour? 2.85 in.
b) What is the total distance the snail has climbed in seven hours? 55.46 in.
( n 1)
7
3
c) Express the total distance with summation notation. 16
4
n 1