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Question 70. If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 – S10).

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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 are given that Sn denotes the sum of the first n terms of an A.P.,

Now we have to prove that S30 = 3(S20 – S10).

CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 70

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1 Answer

  1. Let’s take L.H.S.

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

    Sn = n[2a +(n – 1)d] / 2

    We get

    S30 = 30[2a + (30 – 1)d] / 2

    = 15[2a + 29d]

    R.H.S. = 3(S20 – S10).

    = 3[20[2a + (20 – 1)d] / 2 – 10[2a + (10 – 1)d] / 2]

    = 3[10(2a + 19d) – 5(2a + 9d)]

    = 3[20a + 190d – 10a – 45d]

    = 3[10a + 145d]

    = 3 × 5[2a + 29d]

    = 15[2a + 29d]

    = S30

    Hence proved.

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