[list][*]An arithmetic sequence is one which begins with a [b]first term[/b] ([math]a[/math]) and where each term is separated by a [b]common difference [/b]([math]d[/math]) - eg. [math]5,9,13,17,21,\ldots[/math]. [br][/*][*]A series is the [b]sum[/b] of the terms of a sequence  - eg. [math]5+9+13+17+21+\ldots[/math].[/*][*]The nth term of an arithmetic sequence is given by [math]u_n=a+\left(n-1\right)d[/math][br]The total of the first n terms of an arithmetic series is given by [math]S_n=\frac{n}{2}\left[2a-\left(n-1\right)d\right][/math][/*][/list]

[list][*]An geometric sequence is one which begins with a [b]first term[/b] ([math]a[/math]) and where each term is separated by a [b]common ratio [/b]([math]r[/math]) - eg. [math]5,10,20,40,80,\ldots[/math]. [/*][*]The nth term of an geometric sequence is given by [math]u_n=ar^{n-1}[/math][br]The total of the first n terms of an geometric series is given by [math]S_n=\frac{a\left(1-r\right)^n}{1-r}[/math][br]The [b]sum to infinity[/b] of a convergent geometric series is given by [math]S_{\infty}=\frac{a}{1-r}[/math][/*][/list]