What is the formula for an arithmetic series? Geometric series? Arithmetic sequence? Geometric series?

What do you mean by formula, the sum? finding the nth term?

Here they are anyways:

Finding the n^th term: A_n = A₁ + d * (n - 1)  

S_n = (n/2)*(A₁ + A_n)

d is the common difference, A_n is the n^th term, A₁ is the first term.

For geometric series, there are many difference formulas to find the sum. 

For infinite geometric series, those that don't have an end, (A₁)/(n-1)

For those that do have an end, S_n = [A₁(1-rⁿ)]/(1-r)

r is the common ratio, A₁ is the first term and n is the nth term. 

To find the nth term: 

A_n = AR^n-1