This is a cute reason for why when we count the number of integers in the closed interval [a, b], it's going to be b - a + 1. We setup an arithmetic sequence with initial term a, common difference 1. Now we know that the nth term is a + (n-1)d. So, we get

a + (n-1)d = b(n-1).1 = b - an = b - a + 1