A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. Each prize is Rs 20 less than the preceding prize.
We have to find out the value of each of the prizes.
Let the cost of 1st prize be Rs. P.
Cost of 2nd prize = Rs. P − 20
And the cost of the 3rd prize = Rs. P − 40
We can see that the cost of these prizes are in the form of A.P., having common difference as −20 and first term as P.
Thus, a = P and d = −20
Given that, S7 = 700
We know that the formula of sum of nth term,
Sn = n/2 [2a + (n – 1)d]
7/2 [2a + (7 – 1)d] = 700[ 2a +(-6)(-20)]/2 = 700
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.