Question

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

Answer 1

The odd numbers between 0 and 50 are
\(1, 3, 5, 7, 9 …. \  49\)
Therefore, it can be observed that these odd numbers are in an A.P.
\(a = 1\), \(d = 2\) and \(l = 49\)
\(l = a + (n − 1) d\)
\(49 = 1 + (n − 1)2\)
\(48 = 2(n − 1)\)
\(n − 1 = 24\)
\(n = 25\)
\(S_n = \frac {n}{2} [a+l]\)

\(S_{25} = \frac {25}{2} [1+49]\)

\(S_{25} = \frac {25\times50}{2}\)
\(S_{25} = 25\times25\)
\(S_{25} = 625\)