Question

The sum up to n terms of an AP in which the first term is a, 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 last term i.e. a +(n-1)d equals to l in formulae (1).
Hence, $S_n=\frac{n}{2}(a+l)$