The sum of an arithmetic progression

In short: the arphsum function counts the sum of an arithmetic progression. Does it sound academic? Then it's easier: you set the initial number, the final number, and how many numbers there are between them, and you get the sum. All. arphsum(a, b, c).code>. No extra math, it just works.

a is the first member of the progression, b is the last member of the progression, c is the number of members of the progression

Imagine: You've planned ten workouts, and every next one you do a little more, like +2 push-ups. You can count it yourself. But it's easier to call the function once and not mess with your head. And if training is transferred to tables, analytics, or code, arphsum is generally indispensable.

Why is it needed in everyday life? Just like that:

Finance: Do you save a fixed amount every month? This is already a progression. If you want to know how much you'll save in a year, she'll help you.

Investment: Income is steadily growing by the same amount — it's simple, count through arphsum. You don't have to fold it manually every time.

Engineering: Let's say you have a ladder with the same step between the steps. If you count the total, it's a progression again. And again, arphsum to help.

Physics: Uniform acceleration? It's the same thing: the distances over equal time intervals add up in progression.

Even in sports or cooking: Are you increasing your weekly workload or the number of ingredients by a fixed amount? Yes, yes, it's a progression again.

Here's a real-life example. I started doing push—ups: the first week - 5 times, then every week +2. So what will you be like by week 10?

The first element (a) = 5

Difference (b) = 2

Week number (c) = 10

Result: a + (c - 1) * b = 5 + 9*2 = 23 push-ups

Such calculations are easy to automate — and here's a simple, convenient, working function for you. Without unnecessary words and a mess with formulas. Just arphsum. You set the numbers, and you get the result.

And the further you go, the more you'll encounter this same progression — in your pocket, at a construction site, at a machine, or while jogging. It's just that now you don't have to count it manually.