The penalty for each succeeding day being Rs. 50 more than for the preceding day.
We have to find out how much money the contractor has to pay as penalty, if he has delayed the work by 30 days.
The given penalties are in the form of A.P. having first term as 200 and common difference as 50.
Hence, a = 200 and d = 50
Penalty that has to be paid if contractor has delayed the work by 30 days = S30
By the formula of sum of nth term, we know,
Sn = n/2[2a+(n -1)d]
S30= 30/2[2(200)+(30 – 1)50]
Therefore, the contractor has to pay Rs 27750 as penalty.