A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: rupay 200 for the first day, rupay 250 for the second day, rupay 300 for the third day, etc., the penalty for each succeeding day being rupay 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

The amount paid in the from of penalty is in the from of following AP:
Rs 200, Rs 250, Rs 300, Rs 350, …
Here, a = 200, d = 250 – 200 = 50 and n = 30.
The sum of n terms of an AP is given by
S_n = n/2[2a + (n – 1)d]
⇒ S_30 = 30/2[2(200) + (30 – 1)(50)]
= 15[400 + 1450]
= 15 (1850) = 27750
Hence, the contractor has to pay Rs 27750 as penalty for the delay of 30 days.