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# 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, find the value of each prize.

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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.

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1. ## 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+(71)(20)]

[2a+6(−20)​]/2=100
a+3(20)=100
a60=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.

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