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Deepak Bora
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Asked: 2020-08-02T21:18:05+05:30 In: ,

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

arithmetic progressionexercise 11 bicse & cbse boardquestion no.8rs aggarwal
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    1 Answer

    1. 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)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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