1. Lesson 7-1
Geometric Mean

2. 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.
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, _____, _____, ____
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. 12 12
5. In the geometric sequence 6, ____, 24,... Find the missing term.

4. 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.
Try It:
Find the geometric mean of 3 and 300.
3 , ___ , 300 30

5. 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

6. Therefore ……….. To find the geometric mean between 7 and 28 ...
label the missing term x
7 , ___ , 28
write a proportion
cross multiply
solve

7. Find the geometric mean of . . . Answer = 20 1. 10 and 40
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
and 40
2. 1 and 36
Answer = 6
and 20
Answer = 14.14
4. 5 and 6
Answer = 5.48
and 12.2
Answer = 9.94

8. How does this relate to geometry?

9. The " W " Pattern

10. The Geometric Means Recall the three geometric means that you
discovered from your Sketchpad activity.
BUT FIRST . . .

11. Re-label the Sides (as lengths)

12. Geometric Mean #1 What is the proportion that uses f?
f is the geometric mean of d and e.

13. Geometric Mean #2 What is the proportion that uses b?
b is the geometric mean of e and c.

14. Geometric Mean #3 What is the proportion that uses a?
a is the geometric mean of d and c.

15. Put them all together

16. The “W” Pattern W

17. Try it !
Given: d = 4 and e = 10
Find:
a = ___
b = ___
c = ___
f = ___

18. Solution:
Proportions
Answers

19. Thanks for coming!