Sequences (other)

A sequence is any ordered list of numbers $(a_1, a_2, a_3, ext{...})$. While arithmetic and geometric sequences have simple rules, 'other' sequences may follow more complex or unusual patterns. These can include recursive sequences, alternating sequences, or sequences defined by a formula that does not fit the arithmetic or geometric type.

Important properties

• A sequence can be defined by a formula (explicit) or by a rule that uses previous terms (recursive).

• Some sequences have patterns that change at each step, or depend on the position in the sequence.

• Recognizing the pattern in a sequence is important for predicting future terms.