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

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

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This answer was edited.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)Â²+(a-d)Â²+(a+d)Â²+(a+3d)Â²=216

4aÂ²+20dÂ²=216

aÂ² + 5dÂ² = 54

Putting the value of a

49 + 5dÂ² = 54

5dÂ² = 5

dÂ² = 1

d=Â±1.

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