Question

$\forall n\in N,2\cdot 4^{2n+1}+3^{3n+1}$ is divisible by

• A. $7$
• B. $5$
• C. $11$
• D. $209$

Answer 1

The correct option is C $11$

For $n=1$, we have
$2\cdot 4^{2n+1}+3^{3n+1}=2\times 4^3+3^4=209$, which is divisible by $11$
For $n=2$, we have
$2\cdot 4^{2n+1}+3^{3n+1}=2\times 4^5+3^7=4235$, which is divisible by $11$
Hence, options (c) is true.