Section 11.3 ­­ Geometric Sequences
A geometric sequence is a sequence where the ratio of consecutive terms is a constant.
a, ar, ar2, ar3, ar4, ...
r = common ratio
Example: Are the following sequences geometric?
2, 6, 18, 54, ...
1, 2, 6, 24, 120, ...
Finding the nth term of a geometric sequence
2, 6, 18, 54, ..., n, ...
Formula for the nth term of a geometric sequence
Example: Find a formula for the nth term of the geometric sequence described. Then find the 50th term.
a1 = 2, r = 4
If a3 = 8 and a6 = 64, find a1 and a10
Partial Sums of a Geometric Sequence
pg. 840­841
Formula for the nth partial sum of a geometric sequence:
the nth partial sum of a geometric sequence is given by
Example: Find the sum of the first 8 terms of the geometric sequence with a1 = 6, r = 3.
Infinite Geometric Series
An infinite geometric series is a series of the form a + ar + ar2 + ar3 + ...
Sum of an Infinite Geometric Series
If , then the sum of the infinite geometric series is Example: Find the sum of the infinite geometric sequence: Express the repeating decimal as a fraction: .121212.....