# 9­4 Geometric Sequences and Series Find terms of a ... ... Alg2 Notes 9.4.notebook April 15, 2013 9 4 Geometric Sequences and Series Find terms of a geometric sequence Find geometric

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• Alg2 Notes 9.4.notebook April 15, 2013

9­4 Geometric Sequences and Series

Find terms of a geometric sequence  Find geometric means Find the sums of geometric series

March Madness of Course

I.  Identifying Geometric Sequences

1)  Determine whether the sequence could be  geometric or arithmetic. If possible, find the  common ratio or difference.

Arithmetic Sequence:  common difference (slope) Geometric Sequence:  common ratio (base)

100, 93, 86, 79, ... 180, 90, 60, 15, ... 5, 1, 0.2, 0.04, ...

• Alg2 Notes 9.4.notebook April 15, 2013

II.  Finding the nth term

2)  Find the 7th term of the geometric sequence         3, 12, 48, 192, ....

Step 1:  Find the general equation Step 2:  Plug in 7

12,288

Recursive:

General:  an = a1(r)n­1

III.  Finding the nth Term Given Two Terms

3)  Find the 8th term of the geometric sequence  with a3 = 36 and a5 = 324.

or

The 8th term is 8748 or ­8747.

• Alg2 Notes 9.4.notebook April 15, 2013

IV.  Finding the Geometric Means

Geometric means are the terms between any two  nonconsecutive terms of a geometric sequence.

4) Find the geometric mean of 16 and 25.

= 20

V.  Finding the Sum of a Geometric Series

5)  Find the indicated sum for the geometric series. S8 for 1 + 2 + 4 + 8 + 16 + ...

= 255

• Alg2 Notes 9.4.notebook April 15, 2013

VI.  Application

6)  An online video game tournament begins with 1024  players.  Four players play in each game, and in each game,  only the winner advances to the next round. How many  games must be played to determine the winner?

The final round will have 1  game, so substitute 1 for an.

n = 5 5 rounds to determine the winner.

341 games must be played to determine the winner.

4. Find the geometric mean of 1/2 and 18.                                                    3

40

40

• Alg2 Notes 9.4.notebook April 15, 2013

9.4 p.659  #2 ­ 4, 6 ­ 45 (x3), 46, 47, 55 ­ 57, 59, 67 Major Extra Credit: Using the "Study Guide: Review" for each chapter, make one multiple choice  question for each section and provide the answer­ must be your creation and not  the author's or your neighbor's. Each chapter is worth 2 points under your TEST  category, and must be completed by next MONDAY, April 22nd. Chapter 1 p.43 Chapter 2 p.136 Chapter 3 p.218 Chapter 4 p.298 Chapter 5 p.390 Chapter 6 p.468 Chapter 7 p.528 Chapter 8 p.612 Chapter 9 p.676

Group Quiz Wednesday

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