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Q.
If $n \in N$, then $7^{2 n}+3^{3 n-3} \cdot 3^{n-1}$ is always divisible by
Principle of Mathematical Induction
Solution:
Putting $n=1$ is $7^{2 n}+2^{3 n-3} \cdot 3^{n-1}$, we get
$7^{2.1}+2^{3.1-3} \cdot 3^{1-1}=7^{2} 2^{0} \cdot 3^{0}$
$=49+1=50\,\,\, (1)$
Also, for $n=2$
$7^{2.2}+2^{3.2-3} \cdot 3^{2-1}$
$=2401+24=2425\,\,\,(2)$
From Eq. (1) and (2), it is always divisible by $25$ .