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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 $50$.

Similar Questions

The sum of the first $n$ terms of an $A.P.$ is given by $S_{n} = 7n^{2} - 3n$. Find the $n^{th}$ term of the $A.P.$

The sum of the third and the seventh terms of an $AP$ is $6$ and their product is $8$. Find the sum of the first sixteen terms of the $AP$.

Show that $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ form an $AP$ where $a_{n}$ is defined as $a_{n}=9-5n$. Find the sum of the first $15$ terms.

In an $AP$,if $S_{n} = n(4n + 1)$,find the $AP$.

Find the sum of first $22$ terms of an $AP$ in which $d=7$ and $22^{nd}$ term is $149$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module