Question

Show that the sum of any three consecutive even numbers is divisible by 6.

Answer 1

an even integer is of the form 2n for some integer 'n'.

sum of three consecutive integers is

(2n)+(2n+2)+(2n+4)

2n+2n+2+2n+4

6n+6

6(n+1) - divisible by 6

so the sum of any three consecutive integers is divisible by 6