Question 159
We define a sequence by $a_1 = 850$ and
$$
a_{n+1} = \frac{a_n^2}{a_n - 1}
$$
for $n \ge 1$. Determine all values of $n$ for which $\lfloor a_n \rfloor = 2024$.
$$
a_{n+1} = \frac{a_n^2}{a_n - 1}
$$
for $n \ge 1$. Determine all values of $n$ for which $\lfloor a_n \rfloor = 2024$.