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.

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The Answer of 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.

Suppose That a1=10,a2=5, and an=2an−1+3an−2 for n≥3. a _ { 1 } = 10 , a _ { 2 } = 5 \text {, and } a _ { n } = 2 a _ { n - 1 } + 3 a _ { n - 2 } \text { for } n \geq 3 \text {. }a1​=10,a2​=5, and an​=2an−1​+3an−2​ for n≥3.

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