Notes 6-6
Pre-Cal
Section 9.3 Geometric Sequences
Name:________________________
Describe how the following sequences are generated using words (not an equation!)
-8, -2, 4, 10, 16
2, 6, 18, 54, 162
Geometric Sequence
Formula:
Decide if the following sequences are arithmetic, geometric, or neither.
1 1
1
1
3 9 27 81
 , ,
,
, .....
, ,
, , .....
100, 70, 40, 10,…
2, 8, 18, 32, 50
4 16 64 256
2 2 2 2
Find the term indicated in each of the following geometric sequences.
15th term of sequence where a1 = 20, and r = 1.05
12th term of sequence: 5, 15, 45
Find the rule for the nth term of each geometric sequence. Then find the indicated term.
125
a2 = 24, a5 = 3, find a7
a4 = 125, a10 =
, find a14
64
Decide if arithmetic or geometric. Then find a rule for the nth term.
200, -100, 50, -25,…
ex, e2x, e3x, e4x,…
Finding the sum of a finite geometric sequence
Find the partial sum of the following geometric sequences.
12
 3(.75)
n 1
11
i1
i1
1I
F
G
H3J
K
4 
n 1
–2, 24,-288,….; 5th partial sum
Use summation notation to write the sum of the geometric sequences.
5+15+45+135+…..
6 –12 +24 – 48 +……
Finding the sum of an infinite geometric sequence
Practice

bg
 4 .06
n 1
n 1
F1 I
 5GJ
H2K

n 0
n
3 + .3 + .03 + .003 + …
5 + .5 + .05 + .005 + …
Sequences Study Reference
Arithmetic sequences
Basic rule form:
Sum of a finite arithmetic sequence:
What do the variables represent?
Geometric sequences
Basic rule form:
Sum of a finite geometric sequence:
What do the variables represent?
Sum of an infinite geometric sequence:
How can I tell if a sequence is arithmetic or geometric???
Sequences Study Reference
Arithmetic sequences
Basic rule form:
Sum of a finite arithmetic sequence:
What do the variables represent?
Geometric sequences
Basic rule form:
Sum of a finite geometric sequence:
What do the variables represent?
Sum of an infinite geometric sequence:
How can I tell if a sequence is arithmetic or geometric???