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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