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What's a Sequence?

This one isn't so funny.  If we do some thinking, we'd probably be able to figure it out.  Luckily, we'll be able to get a formula for this kind of sequence later.

OK, so what about this sequence?

-2 , -4 , -4 , -2 , 2 , 8 , ...

Can you find the pattern?

Can you find the next term?

This one's not so simple...  There IS a pattern, but it's a bit buried.

Let's list the differences between the terms and see if that helps.

-2 , -4 , -4 , -2 , 2 , 8 , ___ ... the differences between the terms are -2 , 0 , 2 , 4 , and 6

See what's going on?

-2 , -4 , -4 , -2 , 2 , 8 , ___ ... the differences between the terms are -2 , 0 , 2 , 4 , and 6 ... the differences between the differences between the terms are 2

We're adding 2 each time down here, so just continue with this pattern and work your way back up:

-2 , -4 , -4 , -2 , 2 , 8 , 16 ... the differences of terms are -2 , 0 , 2 , 4 , 6 , and 8 ... the differences between the differences between the terms are 2

We won't be working with these buried guys in later sections, but, they're kind of interesting, so I wanted to show them to you.