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