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  4. For every natural number n, 32n + 2 - 8n - 9 is divisible by

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Q. For every natural number $n, 3^{2n + 2} - 8n - 9$ is divisible by

Principle of Mathematical Induction

Solution:

$3^{2n+1} - 8n - 9, \forall n\in N$
Putting $n = 2$
$\Rightarrow 3^{2 \times 2 + 2} - 8 \times 2 - 9$
$ = 729 - 16 -9$
$= 704$
It is divisible by $16$