# Geometric sequences and series

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

Example

Write the first five terms of a geometric sequence in which
a_{1}=2 and r=3.

We use the first given formula:

Just as with arithmetic series it is possible to find the sum of a geometric series. It is found by using one of the following formulas:

**Videolesson:** use the formula for the sum of a
geometric series to determine the sum when a_{1}=4 and r=2
and we have 12 terms.

**Sequences and series, Binomial theorem**