Cambridge IGCSE Mathematics · Syllabus 0580 · Algebra and Graphs
Sequences
What is Sequences?
An ordered list of numbers generated by a rule, whose nth term is written using subscript notation such as T sub n. A term-to-term rule says how to get from one term to the next; a position-to-term rule gives any term directly from its position. The family is identified from differences: a constant first difference means linear, a constant second difference means quadratic, and a constant third difference means cubic, while a constant ratio between consecutive terms means exponential.
This definition is part of the Algebra and Graphs chapter in Cambridge IGCSE Mathematics.
Sequences in context
Sequence questions are not puzzles to be stared at. There is a reproducible procedure: build a difference table, find the row that becomes constant, and that row names the family. Once you know the family, a short piece of algebra produces the formula. Guessing at patterns works on easy sequences and fails on exactly the ones worth marks.