 In this video we're going to look at quadratic sequences and how to find the nth term for them. You should already know how to find the nth term for arithmetic or linear sequences but if you're unsure you may want to watch that video first. Let's investigate these sequences. The difference changes every time. But now look at the second differences. If the second difference is constant the sequence is quadratic. This means it contains an n squared term. So let's have a look at how to find the nth term of quadratic sequences. We have this sequence. Find the first and second differences. There's a constant second difference so it's going to be n squared. Because the second difference is two it will be one n squared. Always half the second difference. Now write out the original sequence and the one n squared underneath it. Compare the difference. So five to one is four. Eight to four is four. Thirteen to nine is four. And so on. All you need to do is find the nth term of this sequence. And you have your quadratic nth term formula. So it's n squared plus four for this sequence. As always you should check it. So let's have a look at another one. Find the first and second difference. Because the second difference is four the quadratic will be two n squared. Remember that we always half the second difference. Now write out the original sequence and two n squared underneath it. Find the difference between the two. Now you need to find the nth term rule for this. It's n plus two. So the nth term rule for this quadratic sequence is two n squared plus n plus two. And as always check it. So here's two for you to do. Pause the video. Find the nth term. Click play when you're ready. How did you do? So there we have finding the nth term for quadratic sequences. Just remember to look for that second difference and then half it. If you have any questions please comment below. Like and share our videos with your friends.