ยง Arithmetic sequences, number of integers in a closed interval

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 - a
n = b - a + 1