Sequences

A sequence is an ordered list of numbers. It could be made up of integers but it doesn't have to be. I am looking at a GCSE question that gives you a sequence composed of 5 9 13 17 and 21. You are asked to find an expression for the nth term in this sequence. You have to find the pattern. I will look at how to delve deeper into patterns in later blogs but this one does not need a deep explanation. How do you get from 5 to 9? You have to add 4. How do you get from 9 to 13? You add 4. Just follow the sequence and you see that you do this each time.

You have to find the nth term where n can be any number and you know that if n=1 you have 5, so an expression for the nth term has to start 5... The next thing you know is that you add 4 each time so the 2nd term is 5 + 4. Now this is the second term but there is only one lot of 4 not two. So the expression for the nth term is 5 + 4(n-1)

That sums it up