The sum of 1 + 3 + 5 + 7 + dots up to n terms | vedclass

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

Question

(C) The given series is $1, 3, 5, 7, \dots$ which is an Arithmetic Progression $(AP)$.Here,the first term $a = 1$ and the common difference $d = 3 - 1

Vedclass · Accepted Answer

$n^2$

Vedclass · Answer

(C) The given series is $1, 3, 5, 7, \dots$ which is an Arithmetic Progression $(AP)$.Here,the first term $a = 1$ and the common difference $d = 3 - 1 = 2$.The sum of the first $n$ terms of an $AP$ is given by the formula $S_n = \frac{n}{2} [2a + (n - 1)d]$.Substituting the values: $S_n = \frac{n}{2} [2(1) + (n - 1)2]$.$S_n = \frac{n}{2} [2 + 2n - 2]$.$S_n = \frac{n}{2} [2n]$.$S_n = n^2$.

The sum of $1 + 3 + 5 + 7 + \dots$ up to $n$ terms is:

Similar Questions

Find the $n^{th}$ term of the following series: $5, 14, 29, 50, 77, \ldots$

$0.14189189189...$ can be expressed as a rational number.

Find the $25^{th}$ common term of the following $A.P.'s$
$S_1 = 1, 6, 11, .....$
$S_2 = 3, 7, 11, .....$

The sum of all the digits of the numbers from $1$ to $100$ is

The sum of the series $1 + \frac{4}{3} + \frac{10}{9} + \frac{28}{27} + \dots$ up to $n$ terms is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module