This is the basic and conceptual 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 1 and 500 which are multiples of 2 as well as of 5

CBSE DHANPAT RAI publications

Class:- 10th

Solutions of CBSE Mathematics

Question 55(iii)

All integers between 1 and 500 which are multiples of 2 as well as of 5 are 10, 20, 30, 40, . . . .490.

First term(a) = 10, common difference(d) = 20 – 10 = 10 and nth term(a

_{n}) = 490.By using the formula of nth term of an A.P.a_{n}= a + (n – 1)dSo,=> 490 = 10 + (n – 1)10

=> 10(n – 1) = 480

=> n – 1 = 48

=> n = 49

Now by using the formula of sum of n terms of an A.P.S_{n}= n[a + a_{n}] / 2So,S

_{49}= 49[10 + 490] / 2= 49[250]

= 12250