# 11.3 Geometric Sequences and Series

Identify the common ratio of a geometric sequence, and find a given term and the sum of the first

`n`terms.Find the sum of an infinite geometric series, if it exists.

A sequence in which each term after the first is found by multiplying the preceding term by the same number is a **geometric sequence**.

# Geometric Sequences

Consider the sequence:

Note that multiplying each term by 3 produces the next term. We call the number 3 the **common ratio** because it can be found by dividing any term by the preceding term. A geometric sequence is also called a *geometric progression*.

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