Returns using arithmetic and geometric average

Arithmetic
rA = (r1 + r2 + r3 + ...rN) / N
rA = Arithmetic return
r1 = return 1, r2 = return 2, rN = return N, N = total number of returns
Example
rA = ( .10 + .25 - .20 + .25) / 4 = .10 or 10 %

Geometric
rg = {[(1+r1) (1+r2) .... (1+rn)]}^ 1/n - 1 
Example
rg = {[(1.1) (1.25) (.8) (1.25)]}^ 1/4 - 1
    =  (1.5150) 1/4 -1 = .0829 =  8.29%


Note that arithmetic average works better when each number is independent whereas geometric is a better choice if numbers are dependent to each other.
For instance, lets say you are trying to calculate average for annual stock returns over fiver year period. Each year's stock return is not independent of past year's performance. If you incur loss in one year then you have less capital to generate return following year. For this reason, geometric average may give more accurate performance of your portfolio.