I have a recurrence equation $t_n$ which is defined as
$$ t_n=2.5t_{n-1}-1.5t_{n-4},\qquad \text{for }n\geq5 $$
Where $$ \begin{align} t_1&=5\ t_2&=10.5\ t_3&=26.25\ t_4&=62.625 \end{align} $$
I need to solve my recurrence equation for $n$ when $t_n=13\times10^{10}$. How can I achieve this in Sage?