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Check out this sequence:

1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , ...

Can you figure out what the next term will be?  Maybe you saw the pattern right away...  and maybe you didn't

Each term is found by adding the two previous terms:

1 , 1 , 2 ... 1 + 1 = 2


1 , 1 , 2 , 3 ... 1 + 2 = 3


1 , 1 , 2 , 3 , 5 ... 2 + 3 = 5

So, what's the next term?

1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , ___

What's the 50th term?

Hmm...  Not as easy as it was with those squared guys...

Unfortunately, with this guy, you'd have to find all the terms leading up to the 50th term -- since he's based on the two before them and so on.  When this happens, it's called recursion.

By the way, this last sequence is very famous!  It's called the Fibonacci Numbers.  (Named after Fibonacci, of course.)

How about this sequence?

1 , -2 , 4 , -8 , 16 , -32 , ___

Can you guess the next term?

What about the 20th term?