Sequences

In mathematics, sequences are lists of objects (often numbers) that are in a specific order. Generally, there is some sort of relationship between the terms in the sequence. Like sets, sequences can be finite or infinite. Unlike a set, the order of a sequence matters.

Two common types of sequences are arithmetic sequences and geometric sequences. In arithmetic sequences, the difference between any two consecutive terms is always the same. For example, the sequence 1, 3, 5, 7, 9, ... is an arithmetic sequence because the difference between any two consecutive terms is 2. In geometric sequences, the ratio of any two consecutive terms is always the same. For example, the sequence 1, 2, 4, 8, 16, ... is a geometric sequence because the ratio between two consecutive terms is 2.

Many sequences are neither arithmetic nor geometrical. The Fibonacci Sequence is an example of one such sequence.