UNIT 11: STATISTICS, SEQUENCES & SERIES
MA40: ALGEBRA II
11.7 – Geometric Sequences & Series
(Text Ref: Ch 11.3, Pg 667-674)
Standards: MA40-S3C1-01,05
Objective: TSWD analysis of sequences & series by examining a sequence of number, classifying the
sequence as Arithmetic or Geometric & rewriting as a series using sigma notation
GEOMETRIC
SEQUENCES
I.
A.
GEOMETRIC SEQUENCES
Vocabulary
Vocabulary
Sequence –
Sequence
Geometric Sequence –
Common Ratio –
Geometric Sequence
Common Ratio
B.
Identify an
Geometric Sequence
Identifying Geometric Sequences
Decide whether each sequence is arithmetic.
1) 81, 27, 9, 3, 1, …
2) 1, 2, 6, 24, 120, …
C.
Rule for nth term of a Geometric Sequence
D.
Write a rule for the nth term of the sequence.
1. 6, 24, 96, 384, … then find a 7 .
3) 4, -8, 16, -32, …
Rule for Finding
nth Term of an
Geometric Sequence
EXAMPLE #1:
Write a Rule for the
nth Term
2. -8, -12, -18, -27, … then find a 8 .
E.
EXAMPLE #2:
Write a Rule for the
nth Term
Write a rule for the nth term of the sequence. Graph the sequence
1. One term of an geometric sequence is a3  5.
The common raio is r  2.
1
11.7 – Geometric Sequences & Series (continued)
F.
Two terms of a geometric sequence are a2  45 and a5  1215. Find
a rule for the nth term.
II.
A.
GEOMETRIC SERIES
Definition of Geometric Series
Rule for Finding
the Sum of a Finite
Geometric Series
B.
The Sum of a Finite Geometric Series
Example:
Find the Sum of a
Geometric Series
C.
Find each sum.
1. Given the geometric series 1 + 5 + 25 + 125 + 625 + …
a. Find the sum of the first 10 terms.
Example 3:
Write a Rule for the
nth Term
GEOMETRIC SERIES
Definition of
Geometric Series
b. Find n such that S n  3906.
2