Theory:

The odd natural numbers are \(1\), \(3\), \(5\), ….
 
We need to find the value of \(1 + 3 + 5 + … + (2n - 1)\).
 
First term, \(a = 1\).
 
Common difference, \(d = 3 - 1 = 2\).
 
Last term, \(l = 2n - 1\).
 
This series is an \(A.P\).
If the first term \(a\), and the last term \(l\) are given, then Sn=n2[a+l].
Now, substitute the given values in \(S_n\).
 
Sn=n2[1+2n1]
 
Sn=n2×2n
 
\(S_n = n^2\)
 
Therefore, \(S_n = n^2\).
Sum of first \(n\) odd natural numbers \(= n^2\).