One of the most important and exam oriented question from arithmetic progression chapter in which we have to find the value of each prize if a sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize.

Book – RS Aggarwal, Class 10, chapter 5C, question no 45.

## Let the cost of 1st prize be P.

Cost of 2nd prize =P−20

And cost of 3rd prize P−40

It can be observed that the cost of these prizes are in an A.P. having common difference as −20 and first term as P.

a=P,d=−20

Given that,

S7=700

7/2[2a+(7−1)(−20)]

[2a+6(−20)]/2=100

a+3(−20)=100

a−60=100

a=160

Therefore, the value of each of the prizes was Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60 and Rs 40.