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 by
Ans.
Let the First prize be a
then, Second prize = a – 20
third prize = (a – 20) – 20 = a – 40
And so on
hence the sequence will be a, a – 20, a – 40,….
Here,
a = a
d = (a – 20) – a
= a – 20 – a
= -20
∴ the given sequence is an A.P.
Also, Sum of Rs 700 is given, So, Sn = 700
We know that
So,
First prize = a = Rs 160
Second prize = a – 20 = 160 – 10 = Rs 140
Third prize = a – 40 = 160 – 40 = Rs 120
Furth prize = a – 60 = 160 – 60 = Rs 100
Fifth prize = a – 80 = 160 – 80 = Rs 80
Sixth prize = a – 100 = 160 – 100 = Rs 60
Seventh prize = a – 120 = 160 – 120 = Rs 40