It's given the following quadratic relation: $$a_n = \frac{a_{n-1}^2+61}{a_{n-2}}$$ Find $a_{10}$. Note that I can't use a calculator or a computer, instead I was wondering if there's a trick to find it. What can you suggest ?
($a_1 = 7$, $a_2 = 11$)
Sequence $a_n$ satisfies a linear recurrence of order 2.