Chapter 5.8, Problem 5ES

Let $a_0,a_1,a_2,\mathrm{...}$ be the sequence defined by the explicit formula
$a_n=c\cdot 2^{\pi }+D\text{for}\text{each integer }n\ge 0,$
Where C and D are real numbers. Show that for any choice of C and D,
$a_k=3a_{k-1}-2a_{k-2}\text{for}\text{every integer }k\ge 2.$