11.3 Geometric sequences; Geometric Series

A sequence is geometric when the ratio of successive terms is always the same nonzero number. A geometric sequence is defined recursively as The number a is the first term, and the nonzero number r is called the common ratio.

Determine if the following sequence is geometric 3, 15, 75, 375, . . . The sequence is geometric with a common ratio of 5.

Theorem nth Term of a Geometric Sequence For a geometric sequence {an} whose first term is a and whose common ratio is r, the nth term is determined by the formula

Theorem Sum of First n Terms of a Geometric Sequence Let {an} be a geometric sequence with first term a and a common ratio r. The sum Sn of the first n terms of {an} is

Find the sum of the first 10 terms of the following geometric series. That is, find the sum

First term a=1/5, common ratio r=1/5.

Geometric Series

Theorem Sum of an Infinite Geometric Series