Write the sum of three consecutive integers using k, where k = the middle integer of the three?

The first is k - 1, then second is k, and the third is k + 1

--> add them up and collect like terms

k - 1 + k + k + 1 = k + k + k + 1 - 1 = 3k + 0 = 3k

k=1+k+k+1 = 3k

If k is the middle one, then the previous one will be k-1, and the successive one will be k+1.

(k - 1) + (k) + (k + 1)

If you add these together, the -1 and +1 cancel each other out, leaving you with 3k.