if a$\displaystyle _{n+2}$ = (a$\displaystyle _{n+1}$ + a$\displaystyle _n$)/2 for all n greater or equal to 1. show that

a$\displaystyle _n$ converges to (a$\displaystyle _n$ + 2a$\displaystyle _2$)/3.

Please help me. I know that we want to show that the absolute value of a$\displaystyle _n$ minus(a$\displaystyle _n$ + 2a$\displaystyle _2$)/3 is less than epsilon but I am not sure how to get there. Please help.

Ok so am i supposed to know what the first few terms are? can somebody please help me?