I’ve been diving into the world of algorithms and stumbled upon this interesting problem involving the sum of arithmetic progressions. It’s pretty fascinating how math can be so concise yet have fun little twists, right? So here’s the deal:

Imagine you’re tasked with calculating the sum of the first `n` terms of an arithmetic series. You know, the kind where you have a starting number (let’s call it `a`), and then you keep adding a fixed number (let’s say `d`) for each subsequent term. It’s like having a playlist that starts with your favorite song, and each new song has to be a bit different from the one before.

Now, here’s where things get tricky: you want to solve this in the shortest possible Python code. There’s a classic formula to compute the sum, which is \( S_n = \frac{n}{2} \times (2a + (n-1)d) \). Makes sense, right? But I’ve been thinking, could we come up with a shorter way to write this as code?

What I’m really interested in is your approach to tackling this problem. Let’s say someone gives you `n`, `a`, and `d` as inputs. How would you go about calculating the sum of the first `n` terms without it being bulky?

Here’s a challenge for you: Can you come up with the shortest Python function that takes `n`, `a`, and `d` and returns the correct sum? And if possible, could you share your thought process behind your solution? I love seeing how different minds work through the same problem, and I bet there’s a bunch of clever shortcuts or tricks we can learn from one another.

I’d be super curious to see how succinct you can make it! Less is more in this case, and don’t shy away from using Pythonic tricks—like unpacking, list comprehensions, or any other nifty methods that can keep the code clean and short. Let’s see what you’ve got!