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10^n+3(4^(n+2))+5 is divisible by (n in ...

`10^n+3(4^(n+2))+5` is divisible by `(n in N)`

A

7

B

5

C

9

D

7

Text Solution

AI Generated Solution

To prove that \(10^n + 3(4^{n+2}) + 5\) is divisible by 9 for all \(n \in \mathbb{N}\), we will use the principle of mathematical induction. ### Step 1: Base Case We start by checking the base case, \(n = 1\). \[ P(1) = 10^1 + 3(4^{1+2}) + 5 \] ...
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