Question:medium
Find the sum of the odd numbers between 0 and 50.
Find the sum of the odd numbers between 0 and 50.
Updated On: Jan 13, 2026
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Solution and Explanation
The odd numbers from 0 to 50 are
\(1, 3, 5, 7, 9 …. \ 49\).
These odd numbers form an arithmetic progression (A.P.).
The first term is \(a = 1\), the common difference is \(d = 2\), and the last term is \(l = 49\).
Using the formula for the nth term of an A.P., \(l = a + (n − 1) d\), we have:
\(49 = 1 + (n − 1)2\)
\(48 = 2(n − 1)\)
\(n − 1 = 24\)
Therefore, the number of terms is \(n = 25\).
The sum of an A.P. is given by \(S_n = \frac {n}{2} [a+l]\).
Substituting the values:
\(S_{25} = \frac {25}{2} [1+49]\)
\(S_{25} = \frac {25\times50}{2}\)
\(S_{25} = 25\times25\)
\(S_{25} = 625\)
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