A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: for the first day, for the second day, for the third day, etc., the penalty for each succeeding day being more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by days.
As it has been given in the question that the penalty for each succeeding day being more than for the preceding day. This condition is in the form of an Arithematic progression (A.P.) Such that
Where .
Now, we need to find the penalty if the work is delayed by days. Therefore,
We know that the sum of an A.P.
Hence, the total penalty given by the contractor is .