11­3 Geometric Sequences April 22, 2009
11-3 Geometric Sequences
Objective: Identify and generate geometric sequences.
Lesson & Objective
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11­3 Geometric Sequences April 22, 2009
Check Skills You'll Need
Find the next term in each sequence.
1) 1, 2, 4, 8,...
2) 336, 168, 84, 42,...
3) 0.1, 1, 10, 100,...
4) 900, 300, 100,...
Apr 15­2:52 PM
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11­3 Geometric Sequences April 22, 2009
Geometric Sequence
A geometric sequence is a sequence in which the ratio of any term to the term before it is constant.
Are the following sequences arithmetic, geometric, or neither?
1) 5, 15, 45, 135,...
2) 6, ­24, 96, ­384,...
3) 15, 30, 45, 60,...
4) 8, 18, 30, 44,...
Geometric Sequence
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11­3 Geometric Sequences April 22, 2009
Geometric Sequence
A geometric sequence is a sequence in which the ratio of any term to the term before it is constant.
Formula for Geometric Sequences:
a = a r n
(n­1)
1
th
Example:
2, 6, 18, 54, ...
54 18 = 3
18 6 = 3
6 2=3
n
m
ter
m
er
st T
Fir
on
mm
o
C tio
a
R
(n­1)
r=3
a = 2 3
n
Geometric Sequence
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11­3 Geometric Sequences April 22, 2009
(n­1)
a = a r n
1
th
n
m
er
t
s
Fir
m
er
t T
on
m
m
Co atio
R
Example: 4, 12, 36, 108 ...
Geometric Sequence
5
11­3 Geometric Sequences April 22, 2009
Apr 22­12:57 PM
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11­3 Geometric Sequences April 22, 2009
Geometric Mean
You can find the geometric mean of any two positive numbers by taking the positive square root of the product of the two numbers.
geometric mean = √product of the two numbers
You can use the geometric mean to find a missing term of a geometric sequence.
Nov 22 ­ 10:10 AM
7
11­3 Geometric Sequences April 22, 2009
For each sequence find the value of x if the sequence is geometric.
Ex) 20, x, 80
Ex) 5, x, 25
Nov 22 ­ 10:10 AM
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11­3 Geometric Sequences April 22, 2009
HOMEWORK
Page: 614
#'s: 3 ­ 39 multiples of 3
Nov 22 ­ 10:10 AM
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