The first 4 terms of a different sequence are: 9, 13, 17, 21. Find an expression for the nth term of the sequence

In order to find the nth term of a sequence you need to keep the structure of the nth term sequence in mind (dn+x). The first thing we want to do is find 'd'. In this case 'd' stands for difference, which is the difference between each of the terms given. In this case it is 4. Therefore, the sequence must begin '4n'. Then, we can work out the rest of the seuence by applying nth term rules. If 9 is the first term of the sequence then 4(1)+x=9. Therefore x=5 and the nth term sequence looks like this: 4n+5.