For any natural number $n,\left(15 \times 5^{2 n}\right)+\left(2 \times 2^{3 n}\right)$ is divisible by
For any natural number $n,\left(15 \times 5^{2 n}\right)+\left(2 \times 2^{3 n}\right)$ is divisible by
7
11
13
17
Solution
We have, $\left(15 \times 5^{2 n t}\right)+\left(2 \times 2^{3 n t}\right)$
For
$
\begin{aligned}
& \text { For } \begin{aligned}
n & =1, \\
\text { we get } 15 \times 5^2+2 \times 2^3 & =15 \times 25+2 \times 8 \\
& =375+16=391
\end{aligned}
\end{aligned}
$
which is divisible by 17 $\therefore\left(15 \times 5^{2 n}\right)+\left(2 \times 2^{3 n t}\right)$ is divisible by $17, \forall n \in N$