Question

The sum up to $n$ terms of an AP in which the first term is $a$, the last term is $l$, and the common difference is $d$, is ___

• A. $\frac{n}{2}(2a+(n-1\left)d\right)$
• B. $\frac{n}{2}(a+l)$
• C. $\frac{n}{2}(a+(n-1\left)d\right)$
• D. $\frac{n}{2}(2a+l)$

Answer 1

Answer: (A), (B)

The correct options are
A

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

B

$\frac{n}{2}(a+l)$

We know that sum upto n terms of an AP with first term a and common difference d is
$\frac{n}{2}(2a+(n-1\left)d\right)$
$=\frac{n}{2}(a+a+(n-1\left)d\right)$----- (1)
We know that $a+(n-1)d$ is the $n^{th}$ term, which is the last term.
Substituting the value of the last term i.e. $a+(n-1)d$ equals to $l$ in formulae (1).
Hence, $S_n=\frac{n}{2}(a+l)$