Using principle of MI prove that `2.7^n+3.5^n-5` is divisible by 24

Explanation

Let `P(n):2.7^n+3.5^n−5` is divisible by `24`

We note that P(n) is true when `n=1`, since
`2.7+3.5−5=24`. which is divisible by `24`v
Assume that P(k) is true.

i.e. `2.7^k+3.5^k−5=24q`
when `q∈N` `-------------- ( 1 )`

Now, we have to prove that `P(k+1)` is true whenever `P(k)` is true.

We have

`2.7^(k+1)+3.5^(k+1)−5`

`⇒ 2.7^k.7^1+3.5^k.5^1−5`

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