$a_n = r^n a_0 + s \cdot \frac{r^n - 1}{r - 1}$

$a_n = r^n a_0 + \frac{s}{1-r}$

$a_n = r^n \left( a_0 + \frac{s}{1-r} \right) - \frac{s}{1-r}$

$a_n = r^n \left( a_0 - \frac{s}{1-r} \right) + \frac{s}{1-r}$