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Question 55. Find the sum of all integers(iv) from 1 to 500 which are multiples of 2 as well as of 5.

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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 asked to Find the sum of all integers from 1 to 500 which are multiples of 2 as well as of 5.

CBSE DHANPAT RAI publications
CBSE Mathematics Class 10th
Question 55(iv)

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1 Answer

  1. First term(a) = 10, common difference(d) = 20 – 10 = 10 and nth term(an) = 500.

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

    an = a + (n – 1)d

    So, 

    => 500 = 10 + (n – 1)10

    => 10(n – 1) = 490

    => n – 1 = 49

    => n = 50

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

    Sn = n[a + an] / 2

    So, 

    S50 = 50[10 + 500]/2

    = 25[510]

    = 12750

    Hence, sum of all integers from 1 to 500 which are multiples of 2 as well as of 5 is 12750.

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