Ch. 8.1:Geometric Mean

pattern where the next term is found by multiplying the previous term by a factor.

Geometric Sequence

Ex: 1 , 4 , 16 , 64 , 256

What is the factor? 4

Starting number: 2 Factor: 5 Create 4 terms of a geometric sequence.

Try it #1

2 , 10 , 50 , 250

Find the missing term.

2 , ___ , 72 , 432

Try it #2

12

Geometric Mean

The term between any terms of a geometric sequence

ExampleWith a factor of 5, 20 is the geometric mean of 4 and 100.

4 , , 10020

FactConsecutive terms of a geometric sequence are proportional.

a x

x b

•For any geometric sequence: a, x, b

2 6:

6 18ie ie: (2, 6, 18)

Try it !

1. 10 and 40

2. 1 and 36

3. 10 and 20

4. 5 and 6

Find the geometric mean of . . .Answer = 20

Answer = 6

Answer = or 14.14

Answer = or 5.48

10 2

30

How does this relate to geometry?

D CB

A

Re-label the Sides (as lengths)

a bf

d ec

a bf

d e

Geometric Mean #1

af

d e

fb

d

f =

f

e

f is the geometric mean of d and e.

What is the proportion that uses f?

Geometric Mean #2

ba

c e

fb

a bf

d ec

e

b =

b

c

b is the geometric mean of e and c.

What is the proportion that uses b?

Geometric Mean #3

d

a =

a

c

ba

c

af

d

a bf

d ec

a is the geometric mean of d and c.

What is the proportion that uses a?

Put them all together

a bf

d ec

d

a =

a

c

e

b =

b

c

d

f =

f

e

a bf

d ecW

Try it ! Round to hundredth

a bf

d ec

d = 4e = 10

Find:a = ___b = ___c = ___f = ___

Solution:

4

f =

f

10

4

a =

a

14

10

b =

b

14

a bf

4 1014proportions

answers

142a 2 10f 2 35f

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

Name the type of triangle, if possible1) 8, 10, 12

2) 6, 12, 15

3) 13, 19, 6

4) 13, 5, 12

Answer: Acute

Answer: Obtuse

Answer: N.P.

Answer: Right