Sum of m+n terms if sum of m and n terms are given

Sum of m+n terms if sum of m and n terms are given

The sum of $m$ terms of an arithmetic series is $n$, and that of $n$ terms
is $m$. Then how do we calculate the sum of $m+n$ terms?
We know this:
The sum of $p$ terms of an arithmetic series is $\frac{p}{2(2a+(p-1)d)}$
where $a$ is the first term and $d$ is the difference between each term.
We can express what $m$ and $n$ equal to by putting $p$ equal to $n$ and
$m$ respectively.
Then to get $m+n$, we simply add the new ways of expressing $m$ and $n$.
Now to get the sum, we take $p=m+n$, but that yields an expression that is
way too big to handle, and since this is a textbook problem, I am assuming
the answer is short and succint.
Also, can you guys actually show me the example of a series where sum of
$m$ terms is $n$ and vice versa?