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 Arithmetic Sequence: common difference (slope)
Geometric Sequence: common ratio (base)
1) Determine whether the sequence could be geometric or arithmetic. If possible, find the common ratio or difference.
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
Recursive:
General: an = a1(r)n­1
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
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