Question

The first and last terms of an A P. are a and $l$ respectively. If s be the sum of all the terms of the A P., then common difference is

• A. $\frac{l^2-a^2}{2s-(l+a)}$
• B. $\frac{l^2-a^2}{2s-(l-a)}$
• C. $\frac{l^2+a^2}{2s+(l+a)}$
• D. $\frac{l^2+a^2}{2s-(l+a)}$

Answer 1

The correct option is A $\frac{l^2-a^2}{2s-(l+a)}$

First term: $a$

Last term: $l$

$\therefore s=\frac{n}{2}[a+l]$

$\therefore n=\frac{2s}{a+l}$

We know:

$l=a+(n-1)d$

$\therefore d=\frac{l-a}{n-1}=\frac{l-a}{\frac{2s}{a+l}-1}$

$\therefore d=\frac{l^2-a^2}{2s-(l+a)}$

$(Ans\to A)$