Question 8
We define a sequence by $a_{1}=850$ and
$$
a_{n+1} = \frac{a_{n}^{2}}{a_{n}-1}
$$
for $n \geq 1$. Determine all values of $n$ for which $\left\lfloor a_{n}\right\rfloor=2024$.
Here the floor $\lfloor a\rfloor$ of a real number $a$ denotes the largest integer less than or equal to $a$.
$$
a_{n+1} = \frac{a_{n}^{2}}{a_{n}-1}
$$
for $n \geq 1$. Determine all values of $n$ for which $\left\lfloor a_{n}\right\rfloor=2024$.
Here the floor $\lfloor a\rfloor$ of a real number $a$ denotes the largest integer less than or equal to $a$.