Find the sum of all odd numbers between 0 and 50.
Find the sum of all odd numbers between 0 and 50.
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All odd numbers between 0 and 50 are 1, 3, 5, 7,……… 49.
This is an AP in which a = 1, d = (3 - 1) = 2 and \(l=49.\)
Let the number of terms be n.
Then, Tn = 49
\(\Rightarrow\) a + (n - 1) d = 49
\(\Rightarrow\) 1 + (n - 1) x 2 = 49
\(\Rightarrow\) 2n = 50
\(\Rightarrow\) n = 25
∴ Required sum = \(\frac{n}{2}(a+l)\)
= \(\frac{25}{2}[1+49]=25\times25=625\)
Hence, the required sum is 625.
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