Prove that the sum of 3 consecutive integers is divisible by

Prove that the sum of 3 consecutive integers is divisible by 3.

Solution

Let three consecutive interges are x , x+1 and x+2 their difference is 1.

As we can see all are in arithmetic progression for which first term (a ) = x , common difference(d) = 1 .

Sum of first n-terms is given by S_n = n/2[2a+(n-1)d] where a =x, d=1, n=3.

Put all the vaules in given formula S₃ = 3/2[2(x)+(3)] = 3(x+1) = 3* interger which is divisible by 3.