Geometric Mean

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Lesson 7-1
Geometric Mean
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Sequences
Arithmetic Sequence

• Is a pattern of numbers where any term (number in
  the sequence) is determined by adding or
  subtracting the previous term by a constant
  called the common difference.

17 20 23
Example
2, 5, 8, 11, 14, ____, ____, ____
Common difference 3
Geometric Sequence
Is a pattern of numbers where any term (number in
the sequence) is determined by multiplying the
previous term by a common factor.
Example
2, 6, 18, 54, 162, _____, _____, ____
486 1458 4374
Common Factor 3
3
Examples
1. Starting with the number 1 and using a factor
of 4, create 5 terms of a geometric sequence.
1 , 4 , 16 , 64 , 256
2. Starting with the number 2 and using a factor
of 5, create 5 terms of a geometric sequence.
2 , 10 , 50 , 250 , 1250
3. Starting with the number 5 and using a factor
of 3, create 5 terms of a geometric sequence.
5 , 15 , 45 , 135 , 405
4. In the geometric sequence 2, ____, 72, 432,
.Find the missing term.
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5. In the geometric sequence 6, ____, 24,...
Find the missing term.
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Geometric Mean
A term between two terms of a geometric sequence
is the geometric mean of the two terms.
Example
In the geometric sequence 4, 20, 100, .(with a
factor of 5), 20 is the geometric mean of 4 and
100.
Find the geometric mean of 3 and 300.
Try It
3 , ___ , 300
30
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Geometric Mean Fact
Consecutive terms of a geometric sequence are
proportional.
Example
Consider the geometric sequence with a common
factor 10.
4 , 40 , 400
(4)(400) (40)(40)
cross-products are equal
1600 1600
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Therefore ..
To find the geometric mean between 7 and 28 ...
7 , ___ , 28
label the missing term x
write a proportion
cross multiply
solve
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The geometric mean between two numbers a and b is
the positive number x where .
Therefore x .
Try It
Find the geometric mean of . . .
Answer 20
1. 10 and 40
2. 1 and 36
Answer 6
3. 10 and 20
Answer 14.14
4. 5 and 6
Answer 5.48
5. 8.1 and 12.2
Answer 9.94
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How does this relate to geometry?
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The " W " Pattern
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The Geometric Means
Recall the three geometric means that you
discovered from your Sketchpad activity.
BUT FIRST . . .
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Re-label the Sides (as lengths)
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Geometric Mean 1
What is the proportion that uses f?
f is the geometric mean of d and e.
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Geometric Mean 2
What is the proportion that uses b?
b is the geometric mean of e and c.
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Geometric Mean 3
What is the proportion that uses a?
a is the geometric mean of d and c.
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Put them all together
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The W Pattern
W
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Try it !
Given d 4 and e 10
Find a ___ b ___ c ___ f ___
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Solution
Proportions
Answers