Question

Which of the following is the correct relation between nth term and the sum to n terms of an AP ​

Answer 1

$\underline{\textbf{To find:}}$

$\textsf{The relation between n th term and the sum to}$

$\textsf{n terms of an A.P}$

$\underline{\textbf{Solution:}}$

$\textsf{Let the A.P be a,a+d,a+2d, . . . .  .}$

$\mathsf{Then,\;its\;n\;th\;term\;is}$

$\mathsf{t_n=a+(n-1)d\;\;\;and}$

$\mathsf{Sum\;of\;its\;first\;n\;terms\;is}$

$\mathsf{S_n=\dfrac{n}{2}[2a+(n-1)d]}$

$\mathsf{S_n=\dfrac{n}{2}[a+(a+(n-1)d)]}$

$\mathsf{S_n=\dfrac{n}{2}[a+t_n]}$

$\mathsf{2\,S_n=n[a+t_n]}$

$\mathsf{2\,S_n=n\,a+n\,t_n}$

$\implies\boxed{\mathsf{2\,S_n-n\,t_n=n\,a}}$

$\textbf{which is the required relation}$

$\underline{\textbf{Find more:}}$

In an A.P. if Sn = 3n2 - n and its common difference is ‘6’ then first term is ______  

https://brainly.in/question/13374198

In an AP if S20=S40, then what is the value of S60 ?​

https://brainly.in/question/38123552