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Question 27. The first and the last terms of an A.P are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.

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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 the first and the last terms of an A.P are 5 and 45 respectively.

Also it is given that the sum of all its terms is 400,

Now we have to find its common difference

CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 27

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1 Answer

  1. Given A.P. has first term(a) = 5, last term(an) = 45 and sum(Sn) = 400.

    Now by using the formula of sum of n terms of an A.P.

    Sn = n[a + an] / 2

    => 400 = n[5 + 45]/2

    => 25n = 400

    => n = 16

    By using the formula of nth term of an A.P.

    an = a + (n – 1)d

    So,

    => 45 = 5 + (16 – 1)d

    => 15d = 40

    => d = 8/3

    Hence, the common difference of the given A.P. is 8/3.

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