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 natural numbers between 1 and 100 which are divisible by 3.

CBSE DHANPAT RAI publication

CBSE Mathematics Class 10th

Question 48

First odd natural numbers are 1, 3, 5, 7, . . .2n – 1.

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

and nth term(a

_{n}) = 2n – 1.Now by using the formula of sum of n terms of an A.P.S_{n}= n[a + a_{n}] / 2So,= n[1 + 2n – 1] / 2

=2n

^{2 }/ 2= n

^{2}Hence, the sum of first n odd natural numbers is n^{2}.