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

1.	Find the sum of all odd numbers between 0 and 50.
Answer» 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, T_n = 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.

Answer»

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, T_n = 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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