Solution:

The characteristic equation is,

$\begin{array}{r} \\ (\lambda-3)=0 \\\\ \lambda=3 \\ \end{array}$

Hence the homogeneous solution is,

$a_{r}^{(h)}=A(3)^{r} \\ $

Particular solution is of the type P (constant),

$a_{r}=P \\ $

$a_{r-1}=P \\ $

Substituting the value of $a_{r}$ and $a_{r-1}$ in the given recurrence …