Halp :(

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be a sequence of real numbers satisfying $$a_n = a_{n - 1} a_{n + 1}$$ for all $n \ge 2.$ If $a_1 = 1 + \sqrt{7}$ and $a_{1776} = 13 + \sqrt{7},$ then determine $a_{2009}.$