How to Derive the Formula For the Sum of an Arithmetic Series: A Proof of the Sum of a Sequence

In this video we will look at how to derive the formula for the sum of an arithmetic series. I will explain what all of the variables such as a1 and d mean, what an arithmetic series is and how to prove the sum of an arithmetic series formula. The derivation of the sum of an arithmetic series formula is very straightforward when you understand the notation

[georgebeckons]

Process makes complete sense but why does it come out to be the average times n? I feel like we should intuitively expect the result to have something to do with average but it comes as a surprise.