For every natural number n, n^5 + 4n is a multiple of 5 could begin what is the appropriate next step

 The proof is done below.

Step-by-step explanation:  We are given to prove that the following statement is true :

"For every natural number n, is a multiple of 5."

We will prove the above statement by MATHEMATICAL INDUCTION.

Let n = 1. Then, we get

a multiple of 5.

Let n = 2. Then, we get

a multiple of 5.

Let the statement be true for n = m, where m is a natural number.

So,

for any natural number k.

Then,

which is a multiple of 5.

Therefore, if the statement is true for n = m, then it is true for n = m+1.

That is, the statement is true for all natural numbers n.

Hence proved.

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