Arithmetic
General Term:
To figure out the value of any given term (
Sum of Terms:
To figure out the sum of any given arithmetic series (
![s_{n} = [(a+t_{n})n]\div2](http://s0.wp.com/latex.php?latex=s_%7Bn%7D+%3D+%5B%28a%2Bt_%7Bn%7D%29n%5D%5Cdiv2&bg=ffffff&fg=000000&s=0 "s_{n} = [(a+t_{n})n]\div2")
Geometric
General Term:
To figure out any given term (
Sum of Terms:
To figure out the partial sum of any geometric series if not given the last term, the last term, the first term, or the common ratio OR
to do the same thing, but if given the last term of the series.
![S_{n} = [a(r^n-1)]\div (r-1)](http://s0.wp.com/latex.php?latex=S_%7Bn%7D+%3D+%5Ba%28r%5En-1%29%5D%5Cdiv+%28r-1%29&bg=ffffff&fg=000000&s=0 "S_{n} = [a(r^n-1)]\div (r-1)")
You can have two types of geometric series: convergent (terms come closer together) or divergent (terms become further apart).
When you have a convergent series, the common ratio is greater than -1 but smaller than 1 (and cannot equal zero). Convergent series have infinite sums (the number in which the sum of all the terms converge at), which can be calculated with the formula 
Divergent series don’t have infinite sums.