The formula for an arithmetic series is $S_n=\dfrac{n}{2}[2a+(n-1)d]$. With $n\in\mathbb{Z}^{+}$. $a$ is the first term of the sequence and $d$ is the common ratio.
My question is does this formula work if both $a, d\in\mathbb{R}$, or do they have to be integers?
It works with real numbers, complex numbers, rational numbers, quaternions, etc. It involves only finite sums, so it is valid for rings such as polynomials, matrices, etc. and even for structures like vector spaces that only have vector addition and scalar multiplication.
As written the one limitation involves division by two, which is valid except where the "scalar field" is characteristic two. If you need more information about that exception, just ask.