Algebra 2
Unit 8
Name: _______________________________________
Block: __________
Vocabulary:
 Geometric Sequences – A sequence in which each term, after the first, is found by
multiplying by a constant, called the common ratio, r, to the previous term.
o Remember: Division is the same as multiplying by the reciprocal!
Examples:
1.) What are the next four terms?
1 1
, , 1, 2, 4, ______, ______, _______, _______
4 2
What is the common ratio (r) ?
2.) What are the next four terms?
What is the common ratio (r) ?
81, 27, 9, 3, 1, ______, _______, _______, _______
Identifying Geometric Sequences:
Decide whether the sequence is geometric or not? Explain why or why not.
3.) 4, -8, 16, -32, …
4.) 3, 9, -27, -81, 243, …
Rule for a Geometric Sequence:
a1 = first term;
r = common ratio;
an  a1r n1
an = last term
To write a rule, you
need to know:
1.) The first term
2.) The common ratio
Given the Sequence:
3 3 3
, ...
5.) Write a rule for the nth term of the geometric sequence: , ,
4 8 16
Then find a10 .
2
Given The First Term and the Common Ratio:
6.) Write a rule for the nth term of the geometric sequence: a1  16, r 
Given Two Terms:
7.) Write a rule for the nth term of geometric sequence: a1  8, a7 
1
8
Given a Term and the Common Ratio:
8.) Write a rule for the nth term of geometric sequence: a3  5, r  2
Practice: Write a rule for the nth term of the geometric sequence.
a) -4, -16, -64, -256, …(Then find a8).
4
1
b) a1   , r 
5
2
c) a1  1, a6  1024
d) a10  59049, r  3
3
4
3
Geometric Series – Adding the terms of a geometric sequence.
The Sum of a Finite Geometric Series
a1 = first term; r = common ratio;
1  r n
S n  a1 
 1 r
n = # of terms



Before finding a Sum, you
need to know:
1.) The first term (a1)
2.) The common ratio (r)
3.) The number of terms (n)
Examples:
9.) Find the sum of the first 8 terms of the geometric series:
9
10.) Find the sum of the series:
 (2)
4+2+1+…
k 1
k 2
Practice
10
e) Find the sum of the first 10 terms
of the geometric series:
1 + 5 + 25 + 125 + 625 + …
f) Find the sum of the series:
 2(5)
i 1
i 1