Sequences and series

A sequence is an ordered list of numbers. Each term in the sequence is identified by its position in it. A series is the sum of the terms in a sequence. The \(n\)-th term in a series is the sum of the first \(n\) terms in the corresponding sequence.

Generally, a sequence does not need to follow a particular pattern, but we are only mathematically interested in sequences that do follow a certain pattern.

A sequence is defined by stating its first one (or more) terms and the rule by which subsequent terms are calculated. There are many different sequences or classes of sequences, the most common of which are the arithmetic sequence and the geometric sequence.

• Arithmetic sequence and series
• Geometric sequence and series