This is the Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.

Here you have to find the numbers of AP with the help of their given sum and the sum of their square.

Question Number 8 of Exercise 11 B of RS Aggarwal Solution

# Find four numbers in AP whose sum is 28 and the sum of whose squares is 216.

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Let the four numbers be (a-3d), (a-d), (a+d) & (a+3d).

Now A.T.Q

1. Their sum

(a-3d)+(a-d)+(a+d)+(a+3d)=28

4a = 28

a=7.

2.Their product

(a-3d)²+(a-d)²+(a+d)²+(a+3d)²=216

4a²+20d²=216

a² + 5d² = 54

Putting the value of a

49 + 5d² = 54

5d² = 5

d² = 1

d=±1.

Hence, the numbers are 4, 6, 8 & 10