# 19.2 Geometric Sequences

**Geometric Sequence • Common Ratio • Sum of**`n`Terms

A second type of important sequence of numbers is the **geometric sequence** (or **geometric progression**). *In a geometric sequence, each number after the first can be obtained from the preceding one by multiplying it by a fixed number, called the* **common ratio.** We can express this definition in terms of the *recursion formula*

**(19.4)**

where ${a}_{n}$ is any term, ${a}_{n\hspace{0.17em}-\hspace{0.17em}1}$ is the preceding term, and `r` is the common ratio. One important application of geometric sequences is in computing compound interest on savings accounts. Other applications are found in areas such as biology and physics.

# EXAMPLE 1 Illustrations of geometric sequences

The sequence 2, 4, 8, 16, …, is a geometric ...

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