Prove the following by the principle of mathematical induction:`\ 7^(2n)+2^(3n-3). 3^(n-1)` is divisible 25 for all `n in Ndot`

Explanation

Let `P(n)` be the given statement.

Now,

`P(n): 7^{2 n}+2^{3 n-3} cdot 3^{n-1}` is divisible by 25 .

Step1:

`P(1): 7^{2}+2^{3-3} cdot 3^{1-1}=49+1=50`

It is divisible by 25 .

Thus, `P(1)` is true

Step2: Let `P(m)` be true .

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