Question

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

• A. $8$
• B. $15$
• C. $25$
• D. $54$

Answer 1

The correct option is A $8$

Let $a=3^{2n}+7=9^n+7=7+{(1+8)}^n$
$\Rightarrow a=7+1{+}^n{C}_{1}8{+}^n{C}_2{8}^2+...{+}^n{C}_n{8}^n=8(1{+}^n{C}_1{+}^n{C}_{2}8+...{+}^n{C}_n{8}^{n-1})$
Therefore, $a$ is divisible by $8$.
Ans: 8