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Question 26. The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find the common difference.

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One of the most important and exam oriented question from Chapter name- Arithmetic Progression
Class 10th
Chapter number- 9
Exercise :- 9.6
This type of question has been asked in previous years exams.

In this question we have been given that the first and the last terms of an A.P. are 7 and 49 respectively.

Also sum of all its terms is 420

Now we have to  find the common difference

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 26

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1 Answer

  1. Given A.P. has first term(a) = 7, last term(an) = 49 and sum(Sn) = 420.

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

    Sn = n[a + an] / 2

    So,

    => 420 = n[7 + 49]/2

    => 28n = 420

    => n = 15

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

     

     

    an = a + (n – 1)d

    So,

    => 49 = 7 + (15 – 1)d

    => 14d = 42

    => d = 3

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

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