Question 9
Let $n$ be a positive integer. Suppose that $a_1,a_2,a_3,\ldots$ is a sequence of numbers defined by
$$a_1=\sqrt{(n+3)(n-1)+4},\qquad a_k=\sqrt{(n+2k+1)a_{k-1}+4}\quad\text{for }k\ge2.$$
If $a_{100}=2024$, find the value of $n$.
$$a_1=\sqrt{(n+3)(n-1)+4},\qquad a_k=\sqrt{(n+2k+1)a_{k-1}+4}\quad\text{for }k\ge2.$$
If $a_{100}=2024$, find the value of $n$.