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Question 57. If Sn denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 – S4).

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This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.6

In this question we have been given that Sn denotes the sum of first n terms of an A.P.,

Now we have to prove that S12 = 3(S8 – S4)

CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 57

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1 Answer

  1. By using the formula of the sum of n terms of an A.P.

    Sn = n[2a +(n – 1)d] / 2

    So,

    Therefore, L.H.S. = S12 = 12[2a + (12 – 1)d] / 2

    = 6[12a + 11d]

    = 12a + 66d

    R.H.S. = 3(S8 – S4)

    = 3[8(2a + (8 – 1)d) / 2 – 4(2a + (4 – 1)d) / 2]

    = 3[4(2a + 7d) – 2(2a + 3d)]

    = 3[8a + 28d – 4a – 6d]

    = 3[4a + 22d]

    = 12a + 66d

    = L.H.S.

    Hence proved.

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