CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.3 Question 16
16. 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 term, find the value of each of the prizes.
Solution:
It is given that sum of seven cash prizes is equal to Rs 700.
And, Each prize is Rs 20 less than its preceding term.
Let value of first prize = Rs
Let value of second prize =Rs
Let value of third prize = Rs
So, we have sequence of the form:
It is an arithmetic progression because the difference between consecutive terms is constant.
First term = a
Common difference = d = (a-20) – a = -20
n = 7 (Because there are total of seven prizes)
= Rs 700 {given}
Applying formula,
to find sum of n terms of AP , we get
Therefore, value of first prize = Rs 160
Value of second prize = 160 – 20 = Rs 140
Value of third prize = 140 – 20 = Rs 120
Value of fourth prize = 120 – 20 = Rs 100
Value of fifth prize = 100 – 20 = Rs 80
Value of sixth prize = 80 – 20 = Rs 60
Value of seventh prize = 60 -20 = Rs 40
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