8.3 notes.notebook
August 22, 2016
Section 8.3 Geometric Sequences and Series
8.3 notes.notebook
August 22, 2016
Learning Objectives:
1) Find the common ratio of a geometric sequence.
2) Find the terms of a geometric sequence.
3) Use the formula for the general term of a geometric sequence.
4) Learn the recursive definition of a geometric sequence.
5) Use the 2 formulas for geometric series
8.3 notes.notebook
August 22, 2016
A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a common ratio (r).
This common ratio cannot be zero! Recursive Definition of a Geometric Sequence
with first term and common ratio r.
8.3 notes.notebook
August 22, 2016
1) Find the common ratio for each geometric sequence:
a) 3, 9, 27, 81, ... b) 6, ­24, 96, ­384, ...
2) Write the first 4 terms of each geometric sequence:
a) a 1 = 3 and r = ­2 b) a 1 = ­200 and r = ­1/2
3) Determine if each sequence is geometric:
a) 2, 4, 6, 8, ... b) ­4, ­16, ­64, ­256, ...
c) 5, 15, 45, 135, ...
d) 100, 50, 25, 13,...
8.3 notes.notebook
August 22, 2016
The general term of a geometric sequence n­1
is given by
an = a1 r
4a) Find the general term for the sequence where a1 = 3 and r = ­2
8.3 notes.notebook
August 22, 2016
The general term of a geometric sequence n­1
is given by
an = a1 r
4b) Find a6 if a1 = ­200 and r = ­1/2
, , , ...
3c) Find a7 for 3 9 27
4
2 4 8
8.3 notes.notebook
August 22, 2016
Finding the Number of Terms of a Geometric Sequence
Find the number of terms of the geometric sequence
8.3 notes.notebook
Homework:
8.3 Day 1
Pages 680-2: 7-49 eoo
August 22, 2016