Sequence

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A Sequence is a concept from mathematics. It is made up of several things put together, one after the other. The order that the things are in matters: (Blue, Red, Yellow) is a sequence, and (Yellow, Blue, Red) is a sequence, but they are not the same.

There are two kinds of sequences. One kind is finite sequences, which have an end. For example, (1, 2, 3, 4, 5) is a finite sequence. Sequences can also be infinite, which means they keep going and never end. An example of a sequence that is infinite is the sequence of all even numbers, bigger than 0. This sequence never ends: it starts with 2, 4, 6, and so on, and you can always keep on naming even numbers.

If a sequence is finite, it is easy to say what it is: you can just write down all the things in the sequence. This does not work for an infinite sequence. So another way to write down a sequence is to write a rule for finding the thing in any place you want. The rule should tell us how to get the thing in the n-th place, if n can be any number. If you know what a function is, this means that a sequence is a kind of function.

For example, the rule could be that the thing in the n-th place is the number 2×n (2 times n). This tells us what the whole sequence is, even though it never ends. The first number is 2×1, which is 2. The second number is 2×2, or 4. If we want to know the 100-th number, it's 2×100, or 200. No matter which thing in the sequence we want, the rule can tell us what it is.