Find the sum of the odd numbers between 0 and | vedclass

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Question

(C) The odd numbers between $0$ and $50$ are $1, 3, 5, 7, 9, \ldots, 49$.These numbers form an Arithmetic Progression $(A.P.)$ where the first term $a

Vedclass · Accepted Answer

$625$

Vedclass · Answer

(C) The odd numbers between $0$ and $50$ are $1, 3, 5, 7, 9, \ldots, 49$.These numbers form an Arithmetic Progression $(A.P.)$ where the first term $a = 1$,the common difference $d = 2$,and the last term $l = 49$.Using the formula for the $n^{th}$ term: $l = a + (n - 1)d$.$49 = 1 + (n - 1)2$$48 = 2(n - 1)$$n - 1 = 24$$n = 25$.Now,using the sum formula $S_n = \frac{n}{2}(a + l)$:$S_{25} = \frac{25}{2}(1 + 49)$$S_{25} = \frac{25}{2}(50)$$S_{25} = 25 	imes 25 = 625$.

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

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