# Week 16 – Sequences

What are sequences?

It is usually a list of numbers but can also be a list of other things. Each of the objects or numbers in the list are called terms, elements, member meaning all the same thing. If the sequence is to go on forever then it is called an infinite sequence. For sequences that end, they are called finite sequence. Sequences are very similar to a set, where there is an order to each set (does not matter what order) and it sets the same value that appears more than once if it is following the patter. Most sequences have a rule that you must follow to find out the next term in the sequence.

For example, the sequence {3,5,7, 9…} starts at 3 and jumps 3 every time. Even if you are to say that this sequence “starts at 3 and jumps 3 every time” doesn’t help to find out further terms like the 10th, 100th, or the 1000th term in this sequence. So, the rule that you can make is for this sequence is something like 2 times n (the n is the number of the term). However, that won’t work as it is off by one each time. So, if we were to try 2n +1 it would work as a rule.

Here are some examples of patterns that are also known as sequences. 