Question

If $n\in N$, then $3^{4n+2}+5^{2n+1}$ is a multiple of:

• A. $14$
• B. $16$
• C. $18$
• D. $20$

Answer 1

The correct option is A $14$

Given

$3^{4n+2}+5^{2n+1}$

$9^{2n+1}+5^{2n+1}$

When $n=0$

$9^1+5^1=14$

When $n=1$

$9^3+5^3=854=14\left(61\right)$

Hence, $3^{4n+2}+5^{2n+1}$ is a multiple of $14$.