 In this video, we're going to look at arithmetic sequences in more detail. These are also known as linear sequences. We're going to discover how to find the nth term rule, which we will then use to find any term in the sequence. Before we start, you should already know that each number in the sequence is called a term. This is the first term, the second term, and so on. And that this just tells us that the sequence carries on forever. Arithmetic sequences have a common difference. This means that they always go up by the same amount. So the common difference for this sequence is 3. The nth term for this sequence is 3n plus 2. We can use this to generate the sequence. The n stands for what term it is. So the first term, n is 1. Substitute 1 into the formula, 3 times 1 plus 2. For the second term, substitute n equals 2 into the formula. For the fifth term, substitute n equals 5. We can choose any term, the 100th. So here's a question for you. Pause the video, generate the sequence and click play when you're ready. Did you get it right? Look at these two sequences. What do you notice about the common difference and the nth term rule? For arithmetic sequences, the number in front of the n is always the common difference. So because the common difference was minus 5, the nth term rule is minus 5n. Given these sequences, what numbers are missing from their nth term rules? Difference of 4, so the formula is 4n. Difference of minus 3, so the formula is minus 3n. Difference of a half, so the formula is 0.5n. Now looking at the numbers after the n's. Where do these come from? Pause the video and have a think. How do you go from 4 to 2? You have to subtract 2. From negative 3 to 22, you have to add 25. From 0.5 to 1.5, you add 1. So there you have the nth term rule, simple. Here are some questions for you to do. Pause the video, work them out and click play when you're ready. Did you get them right? That's nearly everything you need to know about arithmetic sequences. You know how to find the nth term rule. You can generate a sequence from this rule and you can find any term in the sequence. There's just one more thing we need to discover and that is how to work out if a number is actually in a sequence. So watch part 2 for that. If you liked the video, give it a thumbs up and don't forget to subscribe, comment below if you have any questions. Why not check out our Fusical app as well? Until next time.