A sequence is an ordered list of objects or elements called terms. The terms are often represented using a variable labeled with indices that specify the positions of the terms in the sequence. Depending on the number of terms, a sequence can be finite or infinite. Since it is not possible to list all the elements in an infinite sequence, it is common to place three dots after a few terms. These three dots indicate that the sequence continues indefinitely based on a specific pattern. The values of the terms of a sequence can repeat. Sequences can have all sorts of patterns. The examples below use the same starting term but result in different sequences due to the differences in the patterns. Note that it is common to use letters like $a_n,$ $b_n,$ $c_n,$ and so on to represent distinct sequences.

The pattern of a sequence is essential to understanding its behavior and characteristics. For this reason, sequences are often classified according to their patterns. Sequences $1$ and $2$ are examples of arithmetic sequences and geometric sequences, respectively. Sequence $3$ is the Fibonacci sequence.