The sum of the series 1 + 3 + 5 + 7 + dots up | vedclass

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

Question

(C) The given series is an arithmetic progression with the first term $a = 1$ and the common difference $d = 3 - 1 = 2$.The sum of the first $n$ terms

Vedclass · Accepted Answer

$n^2$

Vedclass · Answer

(C) The given series is an arithmetic progression with the first term $a = 1$ and the common difference $d = 3 - 1 = 2$.The sum of the first $n$ terms of an arithmetic progression is given by the formula $S_n = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values $a = 1$ and $d = 2$ into the formula:$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 the series $1 + 3 + 5 + 7 + \dots$ up to $n$ terms is equal to:

Similar Questions

If the sum of three numbers in an $A.P.$ is $24$ and their product is $440,$ find the numbers.

The four arithmetic means between $3$ and $23$ are.....

The sum of $3+5+7+\ldots$ to $n$ terms is:

The sum of all those terms of the arithmetic progression $3, 8, 13, \ldots, 373$ which are not divisible by $3$ is equal to $.......$.

Three numbers are in $A.P.$ such that their sum is $18$ and the sum of their squares is $158$. The greatest number among them is

Vedclass Test Series

Exam Paper Generator

Online Exam Module