Question

Which of the following numbers is not the sum of three consecutive numbers?
a. 51
b. 61
c. 72
d. 81

Answer 1

Well, here are three consecutive integers: n, n+1, n+2 and when we add them together we get
n + (n+1) + (n+2) = 3n + 3
So now the question is which of the values 51, 61, 72 or 81 cannot be in this form.

So now it comes down to trying them. For example, a. 51: is there an integer n such that
3n + 3 = 51
3n = 48
n = 16
so 51 works.

Try the others until you run into a problem.