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We should introduce a bit of terminology.

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[SOUND].

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What's an arithmetic progression?

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An arithmetic progression is a sequence

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with a common difference between the
terms.

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We should see an example.

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This might begin 5, 12, 19, 26,

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33, and then keep on going.
The general

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form for the nth term will be 5 plus 7n.

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Why is that an arithmetic progression?
Well the difference

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between each term to the next is seven.
Right?

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5 plus 7 is 12 12 plus 7 is 19 19 plus 7
is 26 26 plus 7 is 33, and so on.

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We can write down a general formula for an
arithmetic progression.

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Well, here we go.

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In general,

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a sub n equals some starting number a sub
zero

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plus a common difference times n.
Well, here's another question.

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Why are these things even called
arithmetic progressions?

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Each term Is the arithmetic mean

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of its neighbors.
For

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reals, let's look back at that example.
Yeah, in our

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example, 12 is the arithmetic mean or the
average of 5 and 19.

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So 5 plus 19 is 24, and 24 divided by 2 is
12.

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Same goes for 19, 19 is the arithmetic
mean or the average of its neighbours.

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I'm going to write that down, alright, 19
is the average of 12 and

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26.
What's 12 plus 26?

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It's 38.
And 38 divided

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by 2 is indeed 19.

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