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At a Glance - Sequences

A sequence of numbers is a list of numbers, whether infinite or finite. The individual numbers in a sequence are called terms. If you can wrap your head around a sequence, that may be referred to as "coming to terms with infinity." Or maybe not.

The terms in sequences are separated by commas. Finite sequences have a defined last term. If the sequence is infinite, "..." is written at the end to show that the sequence continues forever. Or that the sequence is lost in thought and trailing off.

For example, 1, 2, 3, 4, 5,... is a sequence. The 1st term is 1, the second term is 2, and so on. This guy's infinite.

And 2, 3, 4 is also a sequence. No little dots means this baby is three and done, but it's still a list of numbers, so it's still a sequence.

Even 0, 0, 0,... is a sequence where every term is 0. And what a scintillating sequence it is.

Because a sequence is a pattern, you can usually find any term of the sequence as long as you're given enough terms to figure out where it's going. If our sequence is all the even natural numbers, for example, we can figure out that the 350th term of the sequence would be 700, since 2 × 350 = 700. Beats writing out the first 350 terms by hand. Unless you're in prison and looking for activities to pass the time.

Sequences also come in handy when we're writing algebraic proofs about different types of numbers. We'll get into that over the next few pages.

Here are some more fun sequences.

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