Question 4
Let $a_{1}=3$, and for $n\gt 1$, let $a_{n}$ be the largest real number such that
$$
4\left(a_{n-1}^{2}+a_{n}^{2}\right)=10 a_{n-1} a_{n}-9
$$
What is the largest positive integer less than $a_{8}$?
$$
4\left(a_{n-1}^{2}+a_{n}^{2}\right)=10 a_{n-1} a_{n}-9
$$
What is the largest positive integer less than $a_{8}$?