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(an) = 2n – 1.
Now by using the formula of sum of n terms of an A.P.
Sn = n[a + an] / 2
So,
= n[1 + 2n – 1] / 2
=2n2 / 2
= n2
Hence, the sum of first n odd natural numbers is n2.