1. Geometric Mean

2. Guess The Next Term

3. Guess The Next Term 2, 6, 18, 54,____ 162 4, 4, 8, 12, 20,____ 32
3, 12, 36, 45, 135, ____
144

4. Arithmetic Sequence , __ , __ , __ 2, 5, 8, 11, 14 17 20 23
The following pattern is called an
arithmetic sequence:
What are the next three terms?
, __ , __ , __
2, 5, 8, 11, 14
Describe this pattern?

5. Geometric Sequence 2, 6, 18, 54, 162 , ___, ___, ___ 486 1458 4374
The following pattern is called an
geometric sequence:
2, 6, 18, 54, 162
What are the three missing
terms?
, ___, ___, ___
Describe this pattern?

6. Definition
A geometric sequence is a pattern of numbers where any term (number in the sequence) is determined by multiplying the previous term by a factor.

7. Example
Starting with the number 1 and using a factor of 4, create 5 terms of a geometric sequence.
1 , 4 , 16 , 64 , 256

8. Try it #1 2 , 10 , 50 , 250 , 1250 Starting with the number 2
and using a factor of 5,
create 5 terms of a geometric sequence.
2 , 10 , 50 , 250 , 1250

9. Try it #2 5 , 15 , 45 , 135 , 405 Starting with the number 5
and using a factor of 3,
create 5 terms of a geometric sequence.
5 , 15 , 45 , 135 , 405

10. Try it #3 2 , ___ , 72 , 432 12 The following is a geometric sequence.
Find the missing term.
2 , ___ , 72 , 432 12

11. Try it #4 6 , ___ , 24 12 The following is a geometric sequence.
Find the missing term.
6 , ___ , 24 12

12. Definition A term between two terms of a geometric sequence is
the geometric mean of the
two terms.

13. Example 4 , , 100 20 In the following geometric sequence
below (with a factor of 5), 20 is the
geometric mean of 4 and 100.
4 , , 100 20

14. Try it #5
Find the geometric mean of 3 and 300.
3 , ___ , 300 30

15. Fact
Consecutive terms of a geometric
sequence are proportional.

16. Example
Geometric Sequence (with a factor of 10):
4 , 40 , 400
cross-products are equal
(4)(400) = (40)(40)
1600 = 1600

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

18. Try it ! Find the geometric mean of . . . Answer = 20 1. 10 and 40

19. How does this relate to geometry?

20. The " W " Pattern

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

22. Re-label the Sides (as lengths)

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

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

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

26. Put them all together

27. The “W” Pattern W

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

29. Solution:
proportions
answers