## Mathematical Analysis## Sequences and Series |

## What is a geometric sequence? |

A geometric sequence—or geometric progression—is a finite or infinite sequence of real numbers with the ratio between two consecutive terms being constant (called the *common ratio* or *r);* in this case, each term is the previous term multiplied by a given number. In a geometric sequence, the formula for the *n*th term, in terms of the first number and the common ratio, becomes:

The first term is *a*_{1}, *r* is the common ratio, and the number of terms is *n*. For example, for the numbers 2, 6, 18, 54, 162, *a*_{1} is 2, *r* is 3, and *n* is 5. The equation then becomes: