Last Updated Sep 27, 2025

Geometric Series Simplified Revision Notes for Leaving Cert Mathematics

Revision notes with simplified explanations to understand Geometric Series quickly and effectively.

Learn about Geometric Sequences & Series for your Leaving Cert Mathematics Exam. This Revision Note includes a summary of Geometric Sequences & Series for easy recall in your Mathematics exam

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Geometric Series

Introduction

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A geometric series is the sum of a geometric sequence.

In general :

$$a+ar+ar^2 + ar^3+ar^4, ...$$

The general term of any arithmetic sequence is

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General term of a geometric series: Page 22

$$S_n=\frac{a(1-r^n)}{1-r}$$

Example

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Find the sum of the first 10 terms in the geometric sequence 64, 32, 16,...

$$\begin{align*} S_{10}&=\frac{(64)(1-(\tfrac{32}{64})^{10})}{1-(\tfrac{32}{64})} \\\\ &=\frac{(64)(1-(\tfrac{1}{2})^{10})}{\tfrac{1}{2}} \\\\ &=\tfrac{1023}{8} \end{align*}$$

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