(A) Given the $n^{th}$ term is $T_n = 2n - 1$. The sum of $n$ terms is given by $S_n = \sum_{k=1}^{n} T_k = \sum_{k=1}^{n} (2k - 1)$. Using the summat

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

(A) Given the $n^{th}$ term is $T_n = 2n - 1$. The sum of $n$ terms is given by $S_n = \sum_{k=1}^{n} T_k = \sum_{k=1}^{n} (2k - 1)$. Using the summation formulas $\sum_{k=1}^{n} k = \frac{n(n+1)}{2}$ and $\sum_{k=1}^{n} 1 = n$,we get: $S_n = 2 \sum_{k=1}^{n} k - \sum_{k=1}^{n} 1$ $S_n = 2 \left( \frac{n(n+1)}{2} \right) - n$ $S_n = n(n+1) - n$ $S_n = n^2 + n - n = n^2$.

Class 11 Mathematics Sequences and Series nth term of special series, Sum to n terms and Infinite number of terms

Easy

If the $n^{th}$ term of a sequence is $T_n = 2n - 1$,then the sum of $n$ terms $S_n = \dots$

A
$n^2$
B
$\frac{n(n+1)}{2}$
C
$\frac{n(n+1)(2n+1)}{6}$
D
$n+2$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Sequences and Series

Subtopic

nth term of special series, Sum to n terms and Infinite number of terms

If $n$ is odd or even,the sum of $n$ terms of the series $1 - 2 + 3 - 4 + 5 - 6 + \dots$ is given by:

Easy

View Solution

If $\sum_{r=1}^{10} r! (r^3 + 6r^2 + 2r + 5) = \alpha(11!)$,then the value of $\alpha$ is equal to ...... .

DifficultJEE MAIN 2021

View Solution

$1 + 3 + 7 + 15 + 31 + \dots$ to $n$ terms =

MediumIIT 1963

View Solution

The mean of $10$ numbers $7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14, \ldots$ is ....... .

DifficultJEE MAIN 2021

View Solution

$\frac{1^3 + 2^3 + 3^3 + 4^3 + \dots + 12^3}{1^2 + 2^2 + 3^2 + 4^2 + \dots + 12^2} = $

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If the $n^{th}$ term of a sequence is $T_n = 2n - 1$,then the sum of $n$ terms $S_n = \dots$

Similar Questions

If $n$ is odd or even,the sum of $n$ terms of the series $1 - 2 + 3 - 4 + 5 - 6 + \dots$ is given by:

If $\sum_{r=1}^{10} r! (r^3 + 6r^2 + 2r + 5) = \alpha(11!)$,then the value of $\alpha$ is equal to ...... .

$1 + 3 + 7 + 15 + 31 + \dots$ to $n$ terms =

The mean of $10$ numbers $7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14, \ldots$ is ....... .

$\frac{1^3 + 2^3 + 3^3 + 4^3 + \dots + 12^3}{1^2 + 2^2 + 3^2 + 4^2 + \dots + 12^2} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module