The sum of the first n terms of an A.P. is gi | vedclass

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

Question

(A) The $n^{th}$ term of an $A.P.$ is given by the formula $T_{n} = S_{n} - S_{n-1}$ for $n > 1$.Given $S_{n} = 7n^{2} - 3n$.Then $S_{n-1} = 7(n-1)^{2

Vedclass · Accepted Answer

$14n - 10$

Vedclass · Answer

(A) The $n^{th}$ term of an $A.P.$ is given by the formula $T_{n} = S_{n} - S_{n-1}$ for $n > 1$.Given $S_{n} = 7n^{2} - 3n$.Then $S_{n-1} = 7(n-1)^{2} - 3(n-1) = 7(n^{2} - 2n + 1) - 3n + 3 = 7n^{2} - 14n + 7 - 3n + 3 = 7n^{2} - 17n + 10$.Now,$T_{n} = (7n^{2} - 3n) - (7n^{2} - 17n + 10) = 7n^{2} - 3n - 7n^{2} + 17n - 10 = 14n - 10$.For $n = 1$,$T_{1} = S_{1} = 7(1)^{2} - 3(1) = 7 - 3 = 4$.Checking the formula $14n - 10$ for $n = 1$,we get $14(1) - 10 = 4$,which matches $T_{1}$.Thus,the $n^{th}$ term is $T_{n} = 14n - 10$ for all $n \geq 1$.

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 $A.P.$

Similar Questions

For the $A.P.$ $-2, -4, -6, \ldots,$ the common difference $d = \ldots$

The ratio of the $11^{\text{th}}$ term to the $18^{\text{th}}$ term of an $AP$ is $2:3$. Find the ratio of the $5^{\text{th}}$ term to the $21^{\text{st}}$ term,and also the ratio of the sum of the first five terms to the sum of the first $21$ terms.

The sum of how many terms of the $A.P.$ $31, 36, 41, \ldots$ is $535$?

If $a=2$ and $d=4,$ then $S_{40}=\ldots \ldots \ldots$

The sum of $n$ terms of an $A.P.$ is given by $S_{n} = 5n^{2} - 3n$. Find the $n^{th}$ term of the $A.P.$

Vedclass Test Series

Exam Paper Generator

Online Exam Module