Question

The first and last terms of an AP are 6 and 12 respectively and also 12 is the 4th term of the AP. The sum of all terms of this AP is ___.

Answer 1

We know that sum to $n$ terms of an AP is $\frac{n}{2}(a+l)$, where $a$ and $l$ are the first and last terms respectively, and $n$ is the number of terms.
As 12 is the 4th term and the last term, we can conclude that this AP contains only 4 terms.
So, the value of $a=6$, $l=12$ and $n=4$
Plugging in the values given, we have, the sum of all terms of this AP $\frac{4}{2}(6+12)=2\times 18=36$