Question

The sum of `n' terms of a finite AP is $\frac{13}{2}$ times the sum of its first and last terms. Which term would be the middle term in this AP?

• A. 9th term
• B. 5th term
• C. 3rd term
• D. 7th term

Answer 1

The correct option is D

7th term

The formula for sum of $n$ terms of an AP is $\frac{n}{2}(2a+(n-1\left)d\right)$.

$2a+(n-1)d=a+a+(n-1)d=a+l$

where $l$ is the $n^{th}$ term or the last term.

If there are $n$ terms in an AP, then the formula for the sum of $n$ terms in an AP would become $\frac{n}{2}(a+l)=\frac{n}{2}(firstterm+lastterm)$.
Now, in the question it is given that the sum of $n$ terms is $\frac{13}{2}$ times the sum of its first and last terms, which means,

$\Rightarrow$$\frac{n}{2}(firstterm+lastterm)=\frac{13}{2}(firstterm+lastterm)$
So, $n=13$ and there are 13 terms in the AP in which the 7th term is the middle term.