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 odd numbers between 100 and 200
CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 50(ii)
All odd numbers between 100 and 200 are 101,103,105,107, . . . 199.
First term(a) = 101,
common difference(d) = 103 – 101 = 2
and nth term(an) = 199.
By using the formula of nth term of an A.P.
an = a + (n – 1)d
So,
=> 199 = 101 + (n – 1)2
=> 2(n – 1) = 98
=> n – 1 = 49
=> n = 50
Now by using the formula of sum of n terms of an A.P.
Sn = n[a + an] / 2
So,
S50 = 50[101 + 199]/2
= 25[300]
= 7500
Hence, the sum of all odd numbers between 100 and 200 is 7500.