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 of the prizes.

Question

Philoid · Accepted Answer

Let p be the first prize awarded to students

Since there are 7 cash prizes, n = 7

So a₁ = x

Then the preceding prizes will be Rs. 20 lesser

So the series will be

p, p-20, p-40,…. p-120.

Since preceding prizes will be Rs. 20 lesser the common difference is 20

The sum of all prizes are given by (s₇) = 700

[2×(p)+(7-1)(-20)] = 700

(2p - 120) = 200

2p = 320

P = 160

So, the each prize cost will be

160, 140, 120, 100, 80, 60, 40