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  4. 10n+3(4n+2)+5 is divisible by (n∈ N) :

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Q. $ {{10}^{n}}+3({{4}^{n+2}})+5 $ is divisible by $ (n\in N) $ :

KEAMKEAM 2005

Solution:

For $ n=1,{{10}^{n}}+{{3.4}^{n+2}}+5 $
$ =10+{{3.4}^{3}}+5=10+192+5 $
$ =207 $
which is divisible by 9.
$ \therefore $ By Induction, the result is divisible by 9.