Question

$\forall n\in N;7\cdot 5^{2n}+12\cdot 6^n$ is divisible by

• A. $13$
• B. $19$
• C. $247$
• D. $26$

Answer 1

The correct option is B $19$

For every $n\in N$ $7.5^{2n}+12.6^n$

For it to be divisible by any number,it should hold true for $n=1$ and $n=2$ and so on...

For $n=1$ we check, $7.5^2+12.6^1=247$

Again, for $n=2$ we check, $7.5^4+12.6^2=4807$

Now from the given options, we can see that the given values for $n=1,n=2$ are divisible by the number $19$ only.