Challenge Level

Try some numbers first - are you convinced?

Can you see how the pictorial and algebraic methods below can be used to explain why the sum of three consecutive numbers is always a multiple of three?

Method 1:

Method 2:

$$n+(n+1) + (n+2) = 3n + 3 = 3(n+1)$$

Try to use similar methods to explain the statements in the problem.