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 $(AP)$ with first term $a = 1$ and common difference $d = 3 - 1 = 2$.Th

Vedclass · Accepted Answer

$n^2$

Vedclass · Answer

(C) The given series is $1, 3, 5, 7, \dots$ which is an Arithmetic Progression $(AP)$ with first term $a = 1$ and 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 $a = 1$ and $d = 2$:$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 sum of odd integers from $1$ to $2001$.

The sums of $n$ terms of three $A.P.'s$ whose first term is $1$ and common differences are $1, 2, 3$ are ${S_1}, {S_2}, {S_3}$ respectively. The true relation is

Let $a_1, a_2, a_3, \ldots$ be in an $A.P.$ such that $\sum_{k=1}^{12} a_{2k-1} = -\frac{72}{5} a_1$,where $a_1 \neq 0$. If $\sum_{k=1}^{n} a_k = 0$,then $n$ is:

If the sum of $n$ terms of an arithmetic progression is $2n^2 + 5n$,then its $n^{th}$ term is.........

The sum of all two-digit positive numbers which,when divided by $7$,yield $2$ or $5$ as a remainder is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module