Question

If $n\in N$, then $3^{2n}+7$ is divisible by

• A. $3$
• B. $8$
• C. $9$
• D. $11$

Answer 1

The correct option is B $8$

$3^{2n}+7={(1+8)}^n+(8-1)$
$=1+8\times n+C(n,2){\times 8}^2+C(n,3){\times 8}^3+......8^n+8-1$
$=8(1+n+C(n,2){\times 8}^1+C(n,3){\times 8}^2+......8^{n-1})$
Hence $8$ is one of its factor.