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Question 11. Find the sum of the first(iii) 51 terms of the A.P. : whose second term is 2 and fourth term is 8.

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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 an arithmetic progression. And we have to find its sum of first 51 terms of the A.P. : whose second term is 2 and fourth term is 8.

CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 11(iii)

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1 Answer

  1. Given A.P. has second term(a2) = 2,

    Fourth term(a4) = 8 and

    number of terms(n) = 51.

    => a2 = a + d

    => 2 = a + d  …(1)

    Also, a4 = a + 3d

    => 8 = a + 3d  … (2)

    Subtracting (1) from (2), we have

    => 2d = 6

    => d = 3

    Putting d = 3 in (1), we get a = −1.

    We know sum of n terms of an A.P. is given by, Sn = n[2a + (n − 1)d] / 2.

    S51 = 51[2(−1) + (51 − 1)(3)]/2

    = 51[−2 + 150]/2

    = 51[74] = 3774

    Hence, the sum of first 51 terms of the given A.P. is 3774.

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