# Geometric sequence

A geometric sequence (also known as a geometric progression) is a sequence of numbers in which the ratio of consecutive terms is always the same.

For example, in the geometric sequence $2$, $6$, $18$, $54$, $162$, …, the ratio is always $3$. This is called the common ratio.

If the first term of the sequence is $a$ and the common ratio is $r$, then the geometric sequence can be written as $a,\ ar,\ ar^2,\ ar^3,\ \dotsc,\ ar^{n-1},\ \dotsc$ which has $n^\text{th}$ term $ar^{n-1}$.