Particular Solution of Recurrence Equation

Question

Given: $S_{n+2} = 13S_{n+1} + 48S_n$ for $\forall n \in N$ I've found the General Solution which is $S_n = A16^n - B3^n$

I don't quite understand how to find the particular solution where $S_0 = 1$ and $S_1=5$. So my question is how do I find the particular solution of this recurrence equation?

Answer 1

$$ S_0 = A - B=1\\ S_1=16A-3B=5 $$

Now solve that system of equations for $A$ and $B$.