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?

Since, work has been delayed by 30 days.

Total Penalty (in ₹) : 200 + 250 + 300 + ……… + upto 30 terms

The above sequence is an A.P. with first term (a) = ₹ 200 and common difference = ₹ 50.

By formula,

Sum upto n terms = S_n = $\dfrac{n}{2}[2a + (n - 1)d]$

Substituting values we get :

$S_{30} = \dfrac{30}{2}[2 \times 200 + (30 - 1) \times 50] \\[1em] = 15 \times [400 + 29 \times 50] \\[1em] = 15 \times [400 + 1450] \\[1em] = 15 \times 1850 \\[1em] = \text{₹ 27750}.$

Hence, total penalty = ₹ 27750.