Hi

i have the recursive sequence which is defined this way:

A(1) = p

A(2) = q

A(n) = 0.5[A(n-1) + A(n-2)]

and i need to prove convergence and find the limit

it is very easy to prove convergence of the sequence from cantor's theorem

it is also possible to see that the limit is L=[p+2q]/3 but i cant manage to prove that this is the limit

please help im going crazy