Q.If $n \in N$, then $7^{2n} + 3^{3n-3}\cdot 3^{n-1}$ is always divisible by:

The Principle of Mathematical Induction (PMI) is a method for proving that a statement $P(n)$, framed for every natural number $n$, is true for all $n \in \mathbb{N}$ at once — without needing to verify infinitely many individual cases directly. It rests on two pillars: a base case, where $P(1)$ (or the smallest relevant value of $n$) is checked directly, and an inductive step, where it is shown that the truth of $P(k)$ forces the truth of $P(k+1)$ for every positive integer $k$. Once both are established, PMI concludes that $P(n)$ holds for every natural number, be …