Sequences and Series

Sequences and Series – Extension Work (IGCSE Further Maths, Chapter 5)

This extension work gives you more practice with real exam questions on arithmetic and geometric series. It is worth 154 marks and is split into colour-coded sections that get harder as you go. Each question shows its grade, its marks and the exam paper it came from.

Starter diagnostic (teal): four quick questions on sums of arithmetic series, sigma notation, sum to infinity and finding the common ratio. Use your score and the table under the starter to decide which section to start at.
Section 1 (red), Grade 5–6: finding the first term, common difference and common ratio, using sigma notation, and using the Sₙ formulas.
Section 2 (blue), Grade 7: forming and solving equations from two conditions, including quadratics in n, and comparing an arithmetic series with a geometric one.
TIF (green), Grade 8: problem solving with logarithms, sums to infinity, convergence, and finding the least value of n.
TIEF (purple), Grade 9: the hardest “show that” questions, using logs and powers of e.