How id recursive sequence different from an arithmetic or geometric sequence?

A recursive sequence defines each term based on one or more preceding terms, often using a specific formula or rule, while arithmetic and geometric sequences rely on a consistent difference or ratio between consecutive terms, respectively. In an arithmetic sequence, each term is generated by adding a fixed constant to the previous term, whereas in a geometric sequence, each term is produced by multiplying the previous term by a constant factor. Recursive sequences can take various forms and do not necessarily follow a linear or exponential pattern. Thus, while all three types of sequences generate ordered sets of numbers, their construction and relationships between terms differ fundamentally.