Page 720 - Algebra 1

L E S S O N Recognizing and Extending Geometric
105
Sequences
Warm Up
New Concepts
1. Vocabulary A(n) __________ is a list of numbers that often follows
(34)
a rule.
Simplify 2. -25
(3)
4. 15(-0.4)2 (4)
3. (-3)4 (3)
5. 3-3
(32)
A geometric sequence is a sequence with a constant ratio between consecutive terms. The ratio between consecutive terms is known as the common ratio. In a geometric sequence, the ratio of any term divided by the previous term is the same for any two consecutive terms.
Math Language
A sequence is a list of numbers that often follows a rule.
geometric sequence: 3, 6, 12, 24, ... ___
ratios: 6 = 12 = 24 3 6 12
Example
1
Finding Common Ratios
Find the common ratio for each geometric sequence. a. 4, 12, 36, 108, ...
SOLUTION
4 12 36 108
_12 _36 _
= 3 = 3 108 = 3
4 12 36 The common ratio is 3.
b. 320, -80, 20, -5, ... SOLUTION
320 -80 20
-80=-1 20 =-1 -5=-1
The common ratio is -_1 . 4
c. 0.4, 1, 2.5, 6.25, ... SOLUTION
0.4
______ 320 4 -80 4 20 4
-5
6.25
_
6.25 =2.5
=2.5 The common ratio is 2.5.
=2.5
2.5
_1 0.4
_2.5 1
1
2.5
Online Connection www.SaxonMathResources.com
Lesson 105 705