# Some more average numbers

Number Theory Level pending

Let $$x_0, x_1, x_2,\ldots$$ be a sequence of a numbers satisfying the recursion,

$x_{n} =\dfrac{x_{n-1} + x_{n-2}}2 ,$

where $$n = 2,3,4 \ldots$$.

If $$x_0 = 0$$ and $$x_1 = 1890$$, find the following:

$\lim_{n \rightarrow \infty} x_n$

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