Adv
deepaksoni
  • 0
Guru

Question 51. Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.

  • 0

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 show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667 by using arithmetic progressions properties.

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 51

Share

1 Answer

  1. Odd integers between 1 and 1000 which are divisible by 3 are 3, 9, 15, . . . .999.

    First term(a) = 3, common difference(d) = 9 – 3 = 6

    and nth term(an) = 999.

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

    an = a + (n – 1)d

    So, 

    => 999 = 3 + (n – 1)6

    => 6(n – 1) = 996

    => n – 1 = 166

    => n = 167

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

    Sn = n[a + an] / 2

    So, 

    S167 = 167[3 + 999] / 2

    = 167[501]

    = 83667

    Hence Proved.

    • 0
Leave an answer

Leave an answer

Browse

Choose from here the video type.

Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs".

Captcha Click on image to update the captcha.

Related Questions