1. Ch. 8.1: Geometric Mean

2. Geometric Sequence Ex: 1 , 4 , 16 , 64 , 256 What is the factor? 4
pattern where the next term is found by multiplying the previous term by a factor.
What is the factor? 4
Ex: 1 , 4 , 16 , 64 , 256

3. Try it #1 2 , 10 , 50 , 250 Starting number: 2 Factor: 5
Create 4 terms of a geometric sequence.
2 , 10 , 50 , 250

4. Try it #2
Find the missing term.
2 , ___ , 72 , 432 12

5. Geometric Mean
The term between any terms
of a geometric sequence

6. Example 4 , , 100 20 With a factor of 5, 20 is the
geometric mean of 4 and 100.
4 , , 100 20

7. Fact Consecutive terms of a geometric sequence are proportional.
For any geometric sequence: a, x, b
ie: (2, 6, 18)

8. Try it ! Find the geometric mean of . . . Answer = 20 1. 10 and 40
Answer = or 14.14
4. 5 and 6
Answer = or 5.48

9. How does this relate to geometry?
The " W " Pattern

10. Re-label the Sides (as lengths)

11. 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.

12. 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.

13. 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.

14. Put them all together W

15. Try it ! Round to hundredth
Find:
a = ___
b = ___
c = ___
f = ___

16. Solution:
proportions
answers

17. Type of Triangle 1: Make sure it is a triangle
a + b > c (where c is the longest side)
2: Acute Triangle: a2 + b2 > c2
Obtuse Triangle: a2 + b2 < c2
Right Triangle: a2 + b2 = c2

18. 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