AP EAMCET · Maths · Mathematical Induction
If \(2\left(4^{2 n+1}\right)+3^{3 n+1}\) is divisible by \(k, k>1\) for all \(n \in N\), then the value of \(k\) is
- A 19
- B 17
- C 11
- D 13
Answer & Solution
Correct Answer
(C) 11
Step-by-step Solution
Detailed explanation
The given expression \(\begin{aligned} & 2\left(4^{2 n+1}\right)+3^{3 n+1}=P(n) \\ & \because \quad P(n)=8\left(4^{2 n}\right)+3\left(3^{3 n}\right) \\ & \text {For } n=1 \text {, } \\ & \because \quad n \in N \\ & P(n=1)=128+81=209 \\ & \end{aligned}\) is divisible by 19 and…
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