# Week 17 – Arithmetic Series

What is an Arithmetic series?

While building onto last week’s topic I did, arithmetic is in the same field of ideas when it comes to sequences. A sequence that ends on a certain number (not infinite) is an arithmetic series. We use arithmetic series to find the sum of all of the numbers in the named sequence. Which sounds easy when it comes to a series that is only five numbers and go up by 2. So you can just do simple adding and it is not likely that you would make any mistakes.  With sequences that are much bigging or the difference between each number is huge, it doesn’t make any sense to add up each number in that sequence. That would take ages and one small error would ruin all of your work.

So how can you find the sum of all of the numbers in a sequence?

WHILE it is all about the patterns! If you are to take the sequence 1,2,3 … 98, 99, 1oo and add the first and last term together, a really cool trick and a pattern is able to be seen. When you are to add  1 and 100, you get the number 101. If you are to do this again the next smallest and next largest term together, you will also get 101. This means in any arithmetic sequence the smallest number and the biggest added together will equal the next smallest and biggest and so on. How can we use this information to find the sum of all of the numbers in a series? You can take the sum of the largest and the smallest number, then multiply that number by the amount of numbers divided by 2 in the series together.

An example of finding the sum: