Sequences and Series
Gr 12

The Grade 12 Sequences and Series module develops learners’ understanding of both arithmetic and geometric patterns, expanding on the foundational sequence work from earlier grades. This chapter introduces the formal techniques used to analyse, compare, and sum terms in a sequence, providing essential skills for examinations and further mathematical study.

Learners begin by revising linear and quadratic patterns before moving into arithmetic and geometric sequences in full detail. The lessons cover deriving the general term TnT_nTn​, determining specific terms, and interpreting the behaviour of each type of sequence. Students also explore arithmetic and geometric series, learning how to calculate the sum of a specific number of terms using the relevant formulas. Particular emphasis is placed on growth, decay, and real-world applications that involve geometric series, such as finance, population models, and repeated percentage changes.

By the end of this module, learners will be able to determine general terms confidently, calculate partial sums for both arithmetic and geometric series, and interpret sequence and series behaviour in both theoretical and applied contexts—equipping them with strong analytical skills for Grade 12 examinations and tertiary-level mathematics.