Ononot — For the recurrence an = 4a{n-1} - 3a{n-2} + 2 \cdot 3^n, the

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Recurrence Relationsmedium

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For the recurrence $a_n = 4a_{n-1} - 3a_{n-2} + 2 \cdot 3^n$ , the homogeneous roots are $r_1 = 3$ and $r_2 = 1$ . Since the forcing term $3^n$ has frequency matching the simple root $r_1 = 3$ , what form should the particular solution $a_n^{(p)}$ take?