Find the sum of the odd numbers between 0 and 50.

The odd numbers between 0 and 50 are 1, 3, 5, 7, 9 … 49.

Therefore, we can see that these odd numbers are in the form of A.P.

Hence,
First term, a = 1
Common difference, d = 2
Last term, l = 49

By the formula of last term, we know,
\(l = a+(n-1) d \)
\(\Rightarrow 49 = 1+(n-1)2 \)
\(\Rightarrow 48 = 2(n -1)\)
\(\Rightarrow n - 1 = 24 \)
\(\Rightarrow \) n = 25 = Number of terms

By the formula of sum of \(n^{th}\) term, we know,

\(S_n = {{n} \over {2}}(a +l)\)
\(S_{25} = {{25} \over {2}} (1+49) \)
\(= {{25(50)} \over {2}} \)
\(=(25)(25) \)
\(= 625\)