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Deepak Bora
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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 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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  1. 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

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