# Converging series

Calculus Level 4

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 $$a+b$$?

×