Question

The first and last term of an A.P. are $a$ and $l$ respectively. If $S$ is the sum of all the terms of the A.P. and the common difference is $\frac{l^{2}-a^{2}}{k-(l+a)}$, then $k$ is equal to

• A. S
• B. 2 S
• C. 3 S
• D. None of these

Answer 1

Answer: (B)

We have, $S=\frac{n}{2}(a+l)$
$ \Rightarrow \frac{2 S}{a+l}=n \,\,\,\, (1)$
Also, $l=a+(n-1) d $
$\Rightarrow d=\frac{l-a}{n-1}$
$=\frac{l-a}{\frac{2 S}{a+l}-1}[$ Using (1) $]$
$=\frac{l^{2}-a^{2}}{2 S-(l+a)}$
$\therefore k=2 S .$