Mathematical Iteration through Computer Programming

Abstract

Mathematical iteration is a process for generating a sequence in which one or more initial terms are given and each subsequent term is determined from its predecessors in the same way. An equation that describes the relationship between a term and its predecessors is called a recurrence relation. Arithmetic and geometric sequences, common topics in high school algebra courses, are examples of iterative processes. Arithmetic sequences are generated iteratively from an initial term, a1, a common difference, d, and a recurrence relation, an+1, = an+ d. Geometric sequences are generated from an initial term, a1 a common ratio, r, and a recurrence relation, an+1 =an •r. Mathematical iteration is used in many other mathematical situations and algorithms, such as the Fibonacci sequence, the Euclidean algorithm, and Newton's method for solving equations.