Ch. 8.1: Geometric Mean

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

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

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

Geometric Mean The term between any terms of a geometric sequence

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

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

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

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

Re-label the Sides (as lengths)

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.

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.

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.

Put them all together W

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

Solution: proportions answers

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 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