A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 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?

**Solution:**

We can see, that the given penalties are in the form of AP with the first term as 200 and the common difference as 50.

Therefore, a = 200 and d = 50

The penalty that has to be paid if the contractor has delayed the work by 30 days = S _{30}

By the formula of the sum of n terms, we know,

S_{n} = n /2[2a + (n – 1) d ]

Therefore,

S _{30}= 30/2[2(200) + (30 – 1)50]

= 15[400 + 1450]

= 15(1850)

= 27750

Therefore, the contractor has to pay ₹ 27750 as a penalty.