Suppose That $a _ { 1 } = 10 , a _ { 2 } = 5 \text {, and } a _ { n } = 2 a _ { n - 1 } + 3 a _ { n - 2 } \text { for } n \geq 3 \text {. }$

Essay

Suppose that $a _ { 1 } = 10 , a _ { 2 } = 5 \text {, and } a _ { n } = 2 a _ { n - 1 } + 3 a _ { n - 2 } \text { for } n \geq 3 \text {. }$ Prove that 5 divides an whenever n is a positive integer.