Adv
deepaksoni
  • 0
Guru

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

  • 0

This is an arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.6
In this question we have to Find the sum of all integers from 1 to 500 which are multiples of 2 or 5.

CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 55(v)

Share

1 Answer

  1. Integers from 1 to 500 which are multiples of 2 are 2, 4, 6, 8, . . . .500.

    First term(a) = 2, common difference(d) = 4 – 2 = 2 and nth term(an) = 500.

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

    an = a + (n – 1)d

    So, 

    500 = 2 + (n – 1)2

    => 2(n–1) = 498

    => n–1 = 249

    => n = 250

    Let S1 be the sum of this A.P. Hence, S1 = 250[2 + 500] / 2 = 125[502] = 62750.

    Integers from 1 to 500 which are multiples of 5 are 5, 10, 15, 20, . . . .500.

    First term(a) = 5, common difference(d) = 10 – 5 = 5 and nth term(an) = 500.

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

    an = a + (n – 1)d

    So, 

    500 = 5 + (n – 1)5

    => (n – 1)5 = 495

    => n – 1 = 99

    => n = 100

    Let S2 be the sum of this A.P. Hence, S2 = 100[5 + 500] / 2 = 50[505] = 25250.

    Integers from 1 to 500 which are multiples of 2 as well as 5 are 10, 20, 30 . . . .500.

    We know, 500 = 10 + (n – 1)10

    => 10(n – 1) = 490

    => n – 1 = 49

    => n = 50

    Let S3 be the sum of this A.P. Hence, S3 = 50[10 + 500] / 2 = 25[510] = 12750.

    Hence, required sum = S1 + S2 – S3

    = 62750 + 25250 – 12750

    = 75250

    • 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