**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**