Unit 3 Cambridge IGCSE Maths Sequences

The main content is divided into eight numbered sections, each with its own clearly numbered subsections:

Introduction to Sequences and Subscript Notation — defines a sequence, introduces unu_n
un​ notation, distinguishes term-to-term from position-to-term rules.
Continuing Sequences and Term-to-Term Rules — recognising and continuing patterns, including sequences with varying differences.
Special Sequences — square, cube, and triangular numbers with their formulae and visual dot representations.
Linear Sequences and the nn
nth Term — finding un=an+bu_n = an + b
un​=an+b, including a worked matchstick pattern problem.
Quadratic Sequences and the nn
nth Term — using second differences to find un=an2+bn+cu_n = an^2 + bn + c
un​=an2+bn+c.
Cubic Sequences and the nn
nth Term — using third differences to find un=an3+bn2+cn+du_n = an^3 + bn^2 + cn + d
un​=an3+bn2+cn+d.
Exponential Sequences — geometric sequences with common ratio rr
r, growth and decay, with a comparison chart.
The Difference Method (Summary and Combinations) — consolidates all techniques into a single decision procedure and introduces combined sequences.