Geometric Sequences Explained for IB Maths
Geometric sequences are a major progression from arithmetic sequences in IB Mathematics: Analysis & Approaches. Instead of changing by a constant difference, geometric sequences change by a constant ratio, making them essential for modelling growth and decay. This topic appears frequently in IB exams and links directly to logarithms, functions, and calculus.
IB students are expected to recognise geometric patterns quickly, write correct general terms, and interpret the behaviour of sequences based on the value of the common ratio. Precision is especially important, as small errors in ratios can dramatically change results.
What Is a Geometric Sequence?
A geometric sequence is a sequence of numbers in which each term is obtained by multiplying the previous term by a constant value called the common ratio. Unlike arithmetic sequences, geometric sequences can grow rapidly or decay toward zero.
In IB Maths, geometric sequences are often presented numerically, algebraically, or in real-world contexts. Students must be comfortable moving between these representations and identifying the common ratio even when terms are not consecutive.
The nth Term Formula for Geometric Sequences
The nth term formula for a geometric sequence allows any term to be calculated directly using the first term and the common ratio. This formula is central to almost every geometric sequence question in IB Maths.
IB exam questions frequently require students to form the nth term using limited information, such as two non-consecutive terms. This requires careful algebraic manipulation and clear logical steps. Students who guess the ratio without verification often lose accuracy marks.
Why Geometric Sequences Matter in IB Maths
Geometric sequences are used to:
- Model exponential growth and decay
- Introduce compound change
- Support geometric series
- Connect algebra to logarithms
- Prepare students for calculus
