Question 6
Define a sequence recursively by $t_1 = 20,$ $t_2 = 21,$ and $$
t_n = \frac{5t_{n-1} + 1}{25t_{n-2}}
$$ for all $n \ge 3.$ Then $t_{2020}$ can be written as $\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p + q.$
t_n = \frac{5t_{n-1} + 1}{25t_{n-2}}
$$ for all $n \ge 3.$ Then $t_{2020}$ can be written as $\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p + q.$