In an A.P.，if the first term $a=7$ ，nth term $a_{n}=84$ and the sum of first $n$ terms $s_{n}=\frac{

Question

In an A.P.，if the first term $a=7$ ，nth term $a_{n}=84$ and the sum of first $n$ terms $s_{n}=\frac{2093}{2}$ ，then $n$ is equal to：\

Professor PC Thomas Classes · Answer

(c) : We have, $a=7$ Let $d$ be the common difference of the A.P.\ and $a_{n}=84$ $\implies $ a+(n-1) d=84 (n-1) d=84-7=77 \Also, $s_{n}=\frac{2093}{2}$\ $\Rightarrow \frac{n}{2}[2 a+(n-1) d]=\frac{2093}{2} \Rightarrow \frac{n}{2}[2 	imes 7+77]=\frac{2093}{2}$\ (using (i))\ $\Rightarrow \quad 91 n=2093 \Rightarrow n=23$ \ Concept Applied - $S_{n}=\frac{n}{2}[2 a+(n-1) d]$