An arithmetic series is just the sum of all of the numbers in an arithmetic sequence. That’s all that it is. Although there are some pretty complex formulas, they require no more than “plug-and-play,” if you know what I mean.
So for example, the arithmetic sequence: 1, 2, 3, 4… is an arithmetic sequence. But an arithmetic series would look like this: 1 + 2 + 3 + 4… . Are you getting the difference?
The symbol that we use when we’re finding the sum of, let’s say, the first 50 terms of an arithmetic series, we write it like this: S50. I think you can understand what the S stands for.
The formula for finding Sn is a lot more complex than the formula for finding an. The formula for Sn = n/2 × (a1 + an). As you can see, it’s a lot more complex than an = a1 + (n – 1)d. So all you have to do is find n (which is always given to you), find an (which can be solved by using the equation), find a1 (which is almost always given to you), and finally, find Sn, which is just solving that formula.
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