Write three consecutive numbers starting with number n+1, where n is natural number. find the sum of those numbers and prove that it is divisible by 3.

Consecutive numbers differ by one, which means that if you start with a certain integer , you obtain the next integer by adding one.

So, if you start with , the three consecutive numbers are

The sum of these three numbers is

This number is divisible by 3 because you can write it as

Note that this is true in general: the sum of three consecutive numbers is always divisible by three, because it is three times the middle number.