Question

A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: $Rs.200$ for the first day, $Rs.250$ for the second day, $Rs.300$ for the third day etc., the penalty for each succeeding day being $Rs.50$ 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?

Answer 1

The money the contractor has to pay as a penalty forms an A.P.

We know,

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$ ............ (Sum of n terms)

$a=$ First term

$d=$ Common difference

$n=$ number of terms

Here,

$a=200,d=50$ and $n=30$

$S_{30}=\frac{30}{2}(400+50\times 29)=27750$