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What's a Sequence?

 

TRY IT:

What's the next number?

2 , 4 , 8 , 16 , ___

These are all sequences.

Here's a casual definition:

A SEQUENCE is a list of numbers
(or other things) that changes
according to some sort of pattern.

With numbers, we usually assign each spot with a special symbol:

a1 , a2 , a3 , a4 , a5 , ... , an , ... Each of these is called a "term." ... a_n is called the nth term.

So, for the sequence of squares that we already saw

1 , 4 , 9 , 16 , 25 , 36 , ...

a1 = 1 , a2 = 4 , a3 = 9 , a4 = 16

What would the 10th term in this sequence be?

a10 = 10^2 = 100

What would  a17  be?

Sometimes it's really easy to find the pattern and find some random nth term like we just did...  and sometimes it isn't.