Final answer:
The term for an ordered arrangement of a set of numbers with specific rules is a sequence. This definition is distinct from patterns, series, and arrays, which have different meanings in mathematics.
Step-by-step explanation:
The term for an ordered arrangement of a set of numbers with specific rules is a sequence. Unlike patterns that suggest a level of predictability without strict adherence to mathematical rules, a sequence follows a precise formula or rule for determining its elements. Likewise, while a series involves the sum of elements, an array is a way to organize data typically in multiple dimensions, neither of which define an ordered set of numbers by specific rules.