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Question 50. Find the sum of (i) all odd numbers between 0 and 50

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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 odd numbers between 0 and 50

CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 50(i)

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1 Answer

  1. All odd numbers between 0 and 50 are 1, 3, 5, 7, . . . 49.

    first term(a) = 1, common difference(d) = 3 – 1 = 2

    and nth term(an) = 49.

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

    an = a + (n – 1)d

    So, 

    => 49 = 1 + (n – 1)2

     

     

    => 2(n – 1) = 48

    => n – 1 = 24

    => n = 25

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

    Sn = n[a + an] / 2

    So, 

    S25 = 25[1 + 49] / 2

    = 25[25]

    = 625

    Hence, the sum of all odd numbers between 0 and 50 is 625.

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