There is one more seat in the back row than in the front row, and n- 1 seat is added in the N-th row, so m-a=n- 1, or m=a+n- 1.

Suppose there are n rows, with an average of (a+m)/2 seats in each row, namely (2a+n- 1)/2, because m=a+n- 1,

So p=(2a+n- 1)*n/2.