A geometric series has first term a a\,a and common ratio rrr, where r≠1r \neq 1r=1. The sum of the first n n\,n terms of the series is SnS_nSn.
By writing down expressions for Sn S_n\,Sn and for rSn rS_n\,rSn and subtracting one from the other, prove that
Sn=a(1−rn)1−rS_n = \dfrac{a(1 - r^n)}{1 - r}Sn=1−ra(1−rn)
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.