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- [Voiceover] What I want to in this video
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is get some practice figuring
out patterns and numbers.
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In particular, patterns that take us from
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one number to a next number in a sequence.
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So over here, in this magenta color,
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I go from 4 to 25 to 46 to 67.
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So what's the pattern here?
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How did I get from 4 to 25
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and can I get the same way from 25 to 46
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and 46 to 67, and I could just
keep going on and on and on?
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Well there's a couple of
ways to think about it.
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When I see 4 and 25, let's see,
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25 isn't an obvious multiple of 4.
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Another way to go from
4 to 25, I could add 21.
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Let's see, if I add 21, 4 plus 21 is 25.
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If I were to go from 25 to 46,
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well I could just add 21 again.
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It looks like to go from
one number to the next
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I'm just adding.
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I wrote 12 by accident, 21.
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I'm just adding 21 over and over again.
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That's going to be 46 plus 21 is 67.
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And if I were to keep going, if I add 21
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I'm going to get to 89.
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If I add 21 to that I'm going to get 110,
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and I could keep going
and going and going.
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I could just keep adding
21 over and over again.
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The pattern here is I'm adding 21.
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Now what about over here, in green?
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When I look at it at first,
it's tempting to say,
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3 plus 3 is 6.
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But then I'm not adding 3 anymore to get
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from 6 to 12, I'm adding 6.
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And then to get from 12 to 24,
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I'm not adding 6 anymore, I added 12.
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So every time I'm adding twice as much.
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But maybe an easier pattern might be,
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another way to go from 3 to 6,
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isn't to add 3, but to multiply it by 2.
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So I multiply by 2 to go from 3 to 6,
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and if I multiply by 2
again, I go from 6 to 12.
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6 times 2 is 12.
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If I multiply by 2 again, I'll go to 24.
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2 times 12 is 24 and I could
keep going on and on and on.
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2 times 24 is 48, 96, I
could go on and on and on.
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The pattern here, it's
not adding a fixed amount,
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it's multiplying each
number by a certain amount,
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by 2 in this case, to get the next number.
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So 3 times 2 is 6, 6 times
2 is 12, 12 times 2 is 24.
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Alright, now let's look at this last one.
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The first two terms here
are the same, 3 and 6.
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The first two numbers here.
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I could say, maybe this is times 2,
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but then to go from 6 to 9,
I'm not multiplying by 2.
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But maybe I am just adding 3 here.
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So 3 to 6, I just added 3.
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Then 6 to 9, I add 3 again,
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and then 9 to 12, I add 3 again.
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So this one actually does look like
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I'm just adding 3 every time.
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The whole point here is to see,
is there something I can do,
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can I do the same something
over and over again
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to get from one number to
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the next number in a sequence like this?
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What you want to make sure
is even if you think you know
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how to go from the first
number to the second number,
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you've got to make sure
that that same way works
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to go from the second
number to the third number,
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and the third number to the fourth number.
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But here we figured it out.
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In this first set of numbers,
we just add 21 every time.
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This one we multiply by 2 every time.
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This one we add 3 every time.