Question

The first and last terms of an AP are 1 and 5 respectively and also 5 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 5 is the 4th term and the last term, we can conclude that this AP contains only 4 terms.
So, the value of a = 1, l = 5 and n = 4.
Plugging in the values given, we have, the sum of all terms of this AP $\frac{4}{2}(1+5)=2\times 6=12$.