A recursive formula is a formula that defines each term of a sequence using the preceding term(s) . Recursive formulas give us two pieces of information: the first term of the sequence and the pattern rule to get any term from the term that comes before it. Recursive formulas are useful for describing sequences that follow a pattern, and they can be used to find any term in the sequence if the previous term is known. Recursive formulas are different from explicit formulas, which directly calculate each term in the sequence and quickly find a specific term. Recursive formulas are expressed in terms of the previous term(s), while explicit formulas express the terms uniquely in terms of the index. Recursive formulas are used in many areas of mathematics, including combinatorics, arithmetic, and geometry.