Name_________________________________
Date___________
GEOMETRIC SEQUENCES
INTRODUCTION TO COLLEGE MATH
In a geometric sequence, you go from one term to the next by multiplying or dividing the same
number each time (we will use the variable r to represent this number that we are multiplying or
dividing).
1. Circle the geometric sequence(s):
a) 3, 7, 11, 14,...
b) 1, 4, 16, 64,...
c) 16, 24, 36, 54,...
d) 1, 3, 6, 12, 24,...
2. Answer the following questions given the sequence 4, 12, 36, 108,...
a) What is the common number
multiplied each time (the r value)
b) Determine the next three terms
of the sequence
3. An geometric sequence is defined by the recursive definition
a1  2
an   an 1  4
.
a) Find the first four terms of this
sequence
b) What is the r value?
c) How many times was 4 multiplied
to 2 to get the
first term:________
second term:_______
third term:________
fourth term:_______
d) Determine a10 (the 10th term)
In the box below, write in a formula that gives you any term (n) of a geometric sequence:
4. The first term of a geometric sequence is 6 and the r value is 3. Find the eighth term.
1
5. Given an geometric sequence in which a1  4096 and r  , find a2 , a3 , and a9
2
6. A geometric sequence is defined by the recursive definition
a) Find the first four terms
a1  2
an  an 1 3
.
b) Find a10
a1  8,192
7. A geometric sequence is defined by the recursive definition
a) Find a4
REVIEW
8. A sequence is defined by
a) Find the first four terms
3.
an  an 1  
2
b) Find a33
a1  4
an  an 1  6
.
b) Find a26
9. Given an arithmetic sequence in which a2  10 and a5  19, find a1 , a12 , and a44
Name_________________________________
Date___________
GEOMETRIC SEQUENCES
INTRODUCTION TO COLLEGE MATH- HOMEWORK
Show ALL WORK
(including for multiple choice)
1. Which of the following sequences is a geometric sequence?
(1) 4, 8, 12, 16,...
(3) 0, 2, 4, 8,...
(2) 5, 10, 30, 120,... (4) 2, 6, 18, 54,...
2. Given a geometric sequence defined by the recursive definition
(1) 27
(2) 6,144
a1  3
an  an 1 2
, find a12 .
(3) 12,288
(4) 24,576
3. Given a geometric sequence 729, 486, 324,...
(a) What is the r value of the sequence
(b) Find the sixth term of the sequence
4. An geometric sequence is defined by the recursive definition
a) Find the first four terms of this
sequence
c) Find a5
a1  1
an   an 1  3
b) What is the r value?
d) Find a8
.
5. The first term of a geometric sequence is 4 and the r value is 5. Find the tenth term.
REVIEW
6. Evaluate the following summations
2
4
j
 1
j1
7. A sequence is defined by the recursive definition
a1  2
an  an 1  3
.
a) Find the first five terms of this
sequence
b) Is this sequence arithmetic?
c) Find
d) Find
8. Given an arithmetic sequence in which a1  3 and a5  31, find a2 , a3 , a4 , and a29