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
- ak = kth term
- r = common ratio
- k = term number
- n = number of terms
- Sn = sum of first n terms of sequence
