A geometric sequence (or geometric progression, GP) is an ordered set of numbers in which the ratio between consecutive values is constant. For example:

2, 6, 18, 54, 162, 486, …

The sum of a sequence is called a series. For example:

2 + 6 + 18 + 54 + 162 + 486 + …

The general term in a geometric sequence is given by

[pmath]a_k = ar^{k-1}[/pmath]

The sum of the first n terms of a geometric sequence is given by

[pmath]S_n = sum{k=1}{n}{ar^{k-1}} = a{1-r^n}/{1-r}[/pmath]

In a convergent series, the sum of the series (an infinite number of terms) is given by

[pmath]S = a/{1-r}[/pmath]

where

- a = first term
- a
_{k}= k^{th}term- r = common ratio
- k = term number
- n = number of terms
- S
_{n}= sum of first n terms of sequence