This is the basic and conceptual question from arithmetic progression chapter in which we are to find the sum of all odd numbers between 0 and 50.
Book RS Aggarwal, Class 10, chapter 5C, question no 12.
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Odd numbers between 0 and 50 are 1,3,5,7,9,....,49
Here, a=1,d=3−1=2,l=49.
We have
l=a+(n−1)d
49=1+(n−1)×2
49−1=2(n−1)⇒2(n−1)=48
n−1=248=24
n=24+1=25
Sum of odd numbers:
Sn=n/2[a+l]
=25/2(1+49)
=25/2(50)
=625.