# Limit of a recursive sequence

Let $\lambda$$\in$$(0,1)$. For any real $a_0$, $a_1$, define the sequence recursively by $$a_n = (1-\lambda)a_{n-1} + \lambda a_{n-2}$$

Let $\alpha$ = $\lim\limits_{n\rightarrow\infty}a_n$

Express the $\alpha$ in terms of $\lambda$, $a_0$ and $a_1$

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