Question

Sum of the first $n$ terms of an A.P. having first term $a$ and last term $\ell$ is ____

• A. $\frac{n}{2}(2a-\ell )$
• B. $\frac{n}{2}(2a+\ell )$
• C. $\frac{n}{2}(a+\ell )$
• D. $\frac{n}{2}(a-\ell )$

Answer 1

The correct option is C $\frac{n}{2}(a+\ell )$

Given: First term of an A.P $=a$

Last term $=2l$

$\therefore$ $l=a+(n-1)d$ $...\left(1\right)$

Sum of $n$ terms $=\frac{n}{2}(2a+(n-1\left)d\right)$

$=\frac{n}{2}(a+a+(n-1\left)d\right)$

$=\frac{n}{2}(a+l)$ [From $\left(1\right)$]