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In this video we are going to look at arithmetic sequences in more detail. These are also known as linear sequences.

We will 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, 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 + 2. We can use this to generate the sequence. The n stands for what term it is.

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 5th term, substitute in n equals 5. We can choose any term… the 100th.

Here’s a question for you to. Pause the video, generate the sequence and click play when you’re ready. Look at these two sequences.

A sequence has an nthterm of -5n + 50
Find the first 5 terms.

1st term = -5(1) + 50 = 45
2nd term = -5(2) + 50 = 40
3rd term = -5(3) + 50 = 35
4th term = -5(4) + 50 = 30
5th term = -5(5) + 50 = 25

45, 40, 35, 30, 25, ...

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 3 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 -3n. Difference of half so formula is 0.5n.

Now looking at the numbers after the n’s… where do these come from?

How do you go from plus 4 to 2? You have to subtract 2. From -3 to 22 you have to add 25. From 0.5 to 1.5 you add 1. And there you have the nth term rule.

Here are some questions for you to do. Pause the video, work them out and click play when you’re ready.

That’s nearly everything you need to know about arithmetic sequences.
You can now find the nth term rule, you know how to generate a sequence from the rule, and you can find any term in the sequence.

All that is left is to discover how we work out if a number is in sequence or not - watch part 2 for that.

CREDITS
Animation & Design: Waldi Apollis
Narration: Lucy Billings
Script: Lucy Billings

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