Question

Consider the nonhomogeneous linear recurrence relation an = 3an−1 + 2^n. Show

that a^n = – 2^(n+1) is a solution of this recurrence relation.

Answer 1

$a_{n-1}=-2^n$

then:

$3a_{n−1} + 2^n=-3\cdot2^n+2^n=2^n(1-3)=-2\cdot2^n=-2^{n+1}=a_n$