D: Sequences and series

Sequences and series form a foundational part of A-Level Mathematics, bridging algebra, calculus, and real-world modelling. A sequence is an ordered list of numbers defined by a rule, while a series is the sum of the terms of a sequence. In the AQA specification, you will explore arithmetic and geometric sequences, their sums, and sigma notation, as well as recurrence relations and modelling with sequences. These concepts are essential for understanding limits, infinite series, and later topics such as binomial expansion and numerical methods.

Mastery of sequences and series is not just about memorising formulas; it requires recognising patterns, manipulating indices, and applying algebraic reasoning. You will learn to find the nth term of a sequence, calculate sums of finite and infinite series, and solve problems involving compound interest, population growth, and depreciation. This topic also introduces the idea of convergence, which is a stepping stone to calculus and analysis.

In the wider A-Level course, sequences and series appear in pure mathematics, statistics (e.g., geometric distributions), and mechanics (e.g., summing forces). Understanding how to sum a series efficiently is a skill that saves time in exams and underpins more advanced topics like Maclaurin series. By the end of this topic, you should be able to confidently handle both arithmetic and geometric progressions, use sigma notation, and apply recurrence relations to model real-life situations.