Mathematics

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

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Sum of odd numbers between 0 and 50 are :

1, 3, 5, …….., 49.

The above list is an A.P. with first term (a) = 1 and common difference (d) = 3 - 1 = 2.

Let 49 be the nth term.

⇒ a_n = 49

⇒ a + (n - 1)d = 49

⇒ 1 + 2(n - 1) = 49

⇒ 2(n - 1) = 48

⇒ n - 1 = $\dfrac{48}{2}$

⇒ n - 1 = 24

⇒ n = 25.

By formula,

Sum of an A.P. (S) = $\dfrac{n}{2}$ [First term + Last term]

Substituting values we get :

$S = \dfrac{25}{2}[1 + 49] \\[1em] = \dfrac{25}{2} \times 50 \\[1em] = 25 \times 25 \\[1em] = 625.$

Hence, sum of the odd numbers between 0 and 50 = 625.

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