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Question 53. Find the sum of all integers between 50 and 500 which are divisible by 7.

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This is an arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.6
In this question we have been asked to Find the sum of all integers between 50 and 500 which are divisible by 7 by using the arithmetic series properties.

CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 53

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1 Answer

  1. All integers between 50 and 500 which are divisible by 7 are 56, 63, 70, 77, . . . . 497.

    First term(a) = 56, common difference(d) = 63 – 56 = 7 and nth term(an) = 497.

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

    an = a + (n – 1)d

    So, 

    => 497 = 56 + (n – 1)7

    => 7(n – 1) = 441

    => n – 1 = 63

    => n = 64

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

    Sn = n[a + an] / 2

    So, 

    S64 = 64[56 + 497] / 2

    = 64[553]

    = 17696

    Hence, the sum of all integers between 50 and 500 which are divisible by 7 is 17696.

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