This is an arithmetic sequence of the form:
a(n)=a+d(n-1), a=initial term, d=common difference, n=term number
The sum of an arithmetic sequence is the average of the first and last terms times the number of terms.
s(n)=(a+a+d(n-1))(n/2)
s(n)=(2a+dn-d)(n/2)
s(n)=(2an+dn^2-dn)/2
We are told that the initial term a=20 and that the common difference, d=2 so:
s(n)=(40n+2n^2-2n)/2
s(n)=(2n^2+38n)/2
s(n)=n^2+19n, so for 4o rows the total number of seats will be:
s(40)=40^2+19(40)
s(40)=1600+760
s(40)=2360
