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 denoted by $S_n,$ and is given as follows:
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$=\frac{n}{2}[a+a+(n-1\left)d\right]$----- (1)
We know that $a+(n-1)d$ is the $n^{\text{th}}$ term, which is the last term, $l$ of an AP of $n$ terms.
Substituting this value of the last term of the AP in (1), we get
$S_n=\frac{n}{2}(a+l).$