## Geometric Sequences

Geometric sequences possesses the simple recursion formula:

a

_{n}= ra_{n-1 }where r is a fixed number known as the common ratio

Sum of the First n Terms

For geometric
sequence {a

Example:

Find the sum of the first ten terms of the geometric sequence: 3, −6, 12, −24, ....

Solution:

Sum of Infinte Geometric Series

_{n}} with first term a_{1}and common ratio r (r ≠ 0, r ≠ 1), the following applies for every positive integer n:Example:

Find the sum of the first ten terms of the geometric sequence: 3, −6, 12, −24, ....

Solution:

Sum of Infinte Geometric Series

For geometric
sequence {a

Examples:

_{n}} with first term a_{1}and common ratio r (|r| < 1), the following appliesExamples: