Sequence limit #1

Calculus Level 3

Consider a recurrence relation \(\{ a_n\}_{n=1}^{n=\infty} \), where \[a_{n+1} = \dfrac{a_n^2 - 5a_n + 10}{5 - a_n} \] for \(n=1,2,3,\ldots\) with \(a_1 = 1\).

Find \(\displaystyle \lim_{n \to \infty} a_n \).

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