Ch' 8'1: Geometric Mean

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Ch. 8.1Geometric Mean
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Geometric Sequence
pattern where the next term is found by
multiplying the previous term by a factor.
What is the factor?
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Ex 1 , 4 , 16 , 64 , 256
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Try it 1
Starting number 2 Factor 5 Create 4 terms of
a geometric sequence.
2 , 10 , 50 , 250
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Try it 2
Find the missing term.
2 , ___ , 72 , 432
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Geometric Mean
The term between any terms of a geometric
sequence
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Example
With a factor of 5, 20 is the geometric mean of
4 and 100.
4 , , 100
20
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Fact
Consecutive terms of a geometric sequence are
proportional.

• For any geometric sequence a, x, b

ie (2, 6, 18)
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Try it !
Find the geometric mean of . . .
Answer 20
1. 10 and 40
2. 1 and 36
Answer 6
3. 10 and 20
Answer or 14.14
4. 5 and 6
Answer or 5.48
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How does this relate to geometry?
The " W " Pattern
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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
W
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Try it ! Round to hundredth
d 4 e 10
Find a ___ b ___ c ___ f ___
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Solution
proportions
answers
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Type of Triangle

• 1 Make sure it is a triangle
• a b gt c (where c is the longest side)
• 2 Acute Triangle a2 b2 gt c2
• Obtuse Triangle a2 b2 lt c2
• Right Triangle a2 b2 c2

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Name the type of triangle, if possible

• 1) 8, 10, 12
• 2) 6, 12, 15
• 3) 13, 19, 6
• 4) 13, 5, 12

Answer Acute
Answer Obtuse
Answer N.P.
Answer Right