# Hotmath Practice Problems

Title:
Hotmath Algebra 2
Author:
Hotmath Team
Chapter:Sequences and SeriesSection:Geometric Sequences and Series

Problem: 1

Determine whether the sequence is arithmetic, geometric, or neither. Give explanation for your answer.

3, 15, 75, 375, ....

Problem: 3

Find the next three terms of the geometric sequence.

243, –81, 27, .....

Problem: 5

Find the geometric mean of the given pair of numbers:

3, 12

Problem: 7

Calculate the missing terms in the geometric sequence, if a1 = 8.1, and a5 = 240.1.

Problem: 9

Find a formula for the nth term of the geometric sequence.

r = 2, a1 = 3

Problem: 11

Find a formula for the nth term of the geometric sequence:

192, –48, 12, –3, ........

Problem: 13

Find a6 of the geometric sequence:

a1 = 4, a3 = 36

Problem: 15

Give a rule for the nth term of the geometric sequence.

a3 = 5, a6 = 200

Problem: 17

Find the nth term of each geometric sequence.

a1 = , n = 10, r = 2

Problem: 19

Find a9 for the geometric sequence.

5, –20, 80, ...

Problem: 21

Find a5 of the geometric sequence:

a2 = 48, a3 = 36

Problem: 23

The given sequence is geometric. Find y.

3, 12, 48, 5y + 7, ...

Problem: 25

Draw the graph of the geometric sequence.

an= 2(6)n – 1

Problem: 27

Find the number of terms in the given geometric series.

1 + b + b2 + b3 +.................b10

Problem: 29

Find the sum of the given geometric series:

n = 20, r = –2, a1 = 1

Problem: 31

Find the sum.

11 + 11 + 11 + ... to 11 terms

Problem: 33

Calculate the sum of the six terms of the geometric series.

4 + 12 + ..... + 972.

Problem: 35

Find Sn, the sum of the first n terms, for the following geometric series.

a1 = 1944, a4 = 1, r = –1/4

Problem: 37

Determine the sum.

Problem: 39

Find the sum of the geometric series:

18 + 6 + 2 + ...

Problem: 41

Obtain the sum of the infinite geometric series, if it has one.

Problem: 43

Write the first three terms of the infinite geometric series that satisfy the condition:

a1 = 6, S = 24

Problem: 45

Write the first three terms of the infinite geometric series that satisfy the condition:

r = –1/2, S = 20

Problem: 47

Calculate the sum of the infinite geometric series.

Problem: 49

Find the sum of the geometric series: a1 = 5, r = 3/5

Problem: 51

Calculate the sum of the infinite geometric series.

Problem: 53

Calculate the sum of the infinite geometric series.

250 + 350 + 490 + 686 +...

Problem: 55

Calculate the fraction form for the repeating decimal 3.111111....