Arithmetic Series are a way to find the sum of a whole group of numbers quickly as long as you have the first and the last number ( & , x being the final term). When you add the first and last number together, you get the sum, and the sum of the rest of the numbers. If you were to add the second number and the second to last number together, you would get the same sum as the first and last! This continues throughout the entire series of numbers.
If you are looking for the sum of all numbers together, you need to do an extra step. You divide the total number of terms by two, and multiply it with the sum of the first and last numbers. When you do this, you get the sum of all the numbers in the entire sequence (or at least the amount of numbers you want from the sequence). This works even if there is an odd number of terms because for example, if it has 19 terms (18 pairs), and 19 divided by 2 is 9.5, the .5 has the missing number inside of it.
This only works with Arithmetic Sequences.