Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · 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 O Level Mathematics (Syllabus D).
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.