Sequence PUMaC
2014

Problem - 2489
Given that $x_{n+2} =\frac{20x_{n+1}}{14x_n}$, $x_0 = 25$, $x_1 = 11$, it follows that $$\sum_{n=0}^{\infty}\frac{x_{3n}}{2^n}=\frac{p}{q}$$ for some positive integers $p, q$ with $GCD(p, q) = 1$. Find $p + q$.