This is an arithmetic progression based 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 0 and 50
CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 50(i)
All odd numbers between 0 and 50 are 1, 3, 5, 7, . . . 49.
first term(a) = 1, common difference(d) = 3 – 1 = 2
and nth term(an) = 49.
By using the formula of nth term of an A.P.
an = a + (n – 1)d
So,
=> 49 = 1 + (n – 1)2
=> 2(n – 1) = 48
=> n – 1 = 24
=> n = 25
Now by using the formula of sum of n terms of an A.P.
Sn = n[a + an] / 2
So,
S25 = 25[1 + 49] / 2
= 25[25]
= 625
Hence, the sum of all odd numbers between 0 and 50 is 625.