Define a sequence recursively by t_{1}=20, t_{2}=21, and

t_{n}=\frac{5 t_{n-1}+1}{25 t_{n-2}}

for all n \geq 3. Then t_{2020} can be written as \frac{p}{q}, where p and q are relatively prime positive integers. Find p+q.

Define a sequence recursively by t_{1}=20, t_{2}=21, and

t_{n}=\frac{5 t_{n-1}+1}{25 t_{n-2}}

for all n \geq 3. Then t_{2020} can be written as \frac{p}{q}, where p and q are relatively prime positive integers. Find p+q.