Why Do Geometric Sequences Model Reality Better Than Arithmetic Ones?
Many IB Mathematics: Applications & Interpretation students notice that exam questions seem to favour geometric sequences over arithmetic ones, especially in finance, population, and modelling contexts. This can feel confusing, particularly if arithmetic sequences feel simpler and more intuitive. The preference is not accidental.
IB uses geometric sequences because they reflect how change actually happens in most real systems. Real-world growth and decay usually depend on the current value, not a fixed amount added each step.
What Geometric Sequences Actually Represent
A geometric sequence models multiplicative change.
Each term is found by multiplying the previous term by a constant factor. This means the amount of change grows or shrinks as the value itself changes. IB expects students to recognise that this structure matches situations where growth is proportional, not fixed.
This proportionality is what makes geometric sequences realistic.
Why Real-Life Change Is Usually Multiplicative
In most real contexts, change scales with size.
Examples include:
- Money earning interest
- Populations growing or shrinking
- Depreciation of assets
- Spread of information or disease
IB expects students to see that a 5% increase depends on how large the quantity already is. Arithmetic sequences cannot capture this behaviour, because they assume the same absolute change every time.
Why Geometric Sequences Feel Harder at First
Geometric growth can feel unintuitive because it accelerates.
Students are often surprised by how quickly values increase or decrease. IB deliberately uses this feature to test whether students understand long-term behaviour and can judge whether results are realistic or extreme.
The discomfort usually comes from unfamiliarity, not difficulty.
Why Arithmetic Models Break While Geometric Models Hold
Over short periods, arithmetic and geometric models can look similar.
Over longer periods, arithmetic models become unrealistic. They may predict negative values, ignore scale, or underestimate growth dramatically. IB expects students to recognise these failures and choose geometric models when proportional change is present.
Choosing a geometric sequence shows stronger modelling judgement.
Why IB Tests Model Choice Explicitly
Applications & Interpretation focuses on decisions, not formulas.
IB wants students to justify why a particular model fits a situation. Choosing a geometric sequence for percentage-based change shows understanding of how the system works, not just how to calculate terms.
Common Student Mistakes
Students frequently:
- Use arithmetic sequences for percentage change
- Avoid geometric models due to complexity
- Fail to justify model choice
- Ignore long-term implications
- Accept unrealistic outputs
Most errors come from choosing comfort over correctness.
How IB Expects You to Use Geometric Sequences
IB expects students to:
- Identify proportional change
- Use growth or decay factors correctly
- Match factors to time units
- Interpret long-term behaviour
- Discuss limitations of the model
Marks are often awarded for explanation rather than calculation.
Exam Tips for Choosing the Right Model
Ask whether the change depends on the current value. Look for words like percentage, rate, or per year. Compare predictions over time. Justify your choice clearly — IB rewards reasoning.
Frequently Asked Questions
Are geometric sequences always better than arithmetic ones?
No. They are better when change is proportional. IB expects students to decide based on context.
Why does IB prefer geometric models in finance?
Because finance involves percentage growth and decay. Geometric sequences reflect this reality accurately.
Can I lose marks for choosing the wrong model?
Yes. Even perfect calculations lose marks if the model is inappropriate. IB values judgement over mechanics.
RevisionDojo Call to Action
Geometric sequences model reality better because real change is rarely linear. RevisionDojo helps IB Applications & Interpretation students choose models intelligently, justify assumptions, and explain results clearly — exactly what examiners reward. If modelling questions feel unpredictable, RevisionDojo is the best place to build confident decision-making skills.
