I have no problem showing that this is indeed convergent, as it is obviously Cauchy. I am having difficulty showing what it converges to.
Let $a_{0}$ and $a_{1}$ be any two real numbers, and define $$ a_{n}=\frac{a_{n-1}+a_{n-2}}{2} $$ Determine the convergence of the sequence $\left\{a_{n}\right\}$
I searched but could not find this previously asked. Now in the sidebar I see that this is a duplicate.
Determine the convergence of a sequence given by $a_n= \frac{a_{n-1} + a_{n-2}}2$
Limit of sequence in which each term is defined by the average of preceding two terms
