Converging series

Calculus Level 3

Let \(x_n\) be a sequence of real numbers satisfying the recursion relation

\[\large x_n = \frac{x_{n-1}}{8} + 3 \]

If \( \displaystyle \lim_{n\to\infty} x_n = \dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is \(a+b\)?

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