Arithmetic sequences are usually one of the first pattern-based topics students learn, which makes them feel familiar and safe. Because of this, many IB Mathematics: Applications & Interpretation students instinctively reach for arithmetic sequences when modelling real situations. However, these models often fail to reflect reality, and IB examiners frequently penalise their misuse.
IB includes arithmetic sequences to show their limitations, not just their mechanics. The key issue is that arithmetic sequences assume constant additive change, which rarely matches how real systems behave.
What Arithmetic Sequences Actually Model Well
An arithmetic sequence models situations where the change between terms is constant.
This works well for:
- Fixed increases or decreases
- Simple patterns over short time frames
- Controlled, artificial scenarios
IB expects students to recognise that arithmetic sequences describe linear change, not growth or decay.
Why Real-Life Situations Rarely Change Linearly
Most real-world processes do not increase or decrease by a fixed amount.
Population growth, finance, depreciation, and resource use usually involve percentage change, not constant addition. IB deliberately includes modelling questions where arithmetic sequences produce unrealistic predictions over time, testing whether students can recognise when a model is inappropriate.
Why Students Default to Arithmetic Sequences
Arithmetic sequences feel simpler and more intuitive than geometric ones.
Students often choose them because:
- They avoid compounding
- They feel easier to calculate
- They resemble earlier school maths
IB uses this tendency to test judgement. Choosing an arithmetic model when growth is proportional signals weak interpretation.
Why Arithmetic Models Break Down Quickly
Even when arithmetic sequences appear reasonable at first, they often fail over longer periods.
IB expects students to recognise that linear growth can lead to impossible results, such as negative populations or constant increases that ignore scale. Spotting these flaws is part of the assessment.
Why IB Tests This Explicitly in AI Maths
Applications & Interpretation prioritises realistic modelling.
IB wants students to question assumptions, not apply formulas blindly. Recognising when an arithmetic sequence is not suitable is just as important as using one correctly.
Common Student Mistakes
Students frequently:
- Use arithmetic sequences for percentage growth
- Ignore compounding effects
- Accept unrealistic long-term predictions
- Fail to justify model choice
- Avoid discussing limitations
Most mistakes come from choosing convenience over realism.
How IB Expects You to Handle Sequence Modelling
IB expects students to:
- Identify the type of change involved
- Justify why a model is appropriate
- Recognise limitations of linear models
- Compare arithmetic and geometric behaviour
- Interpret results realistically
Marks are often awarded for explanation, not calculation.
Exam Tips for Modelling with Sequences
Ask whether change is additive or multiplicative. Check whether growth depends on the current value. Test whether predictions remain realistic over time. Explain why you chose a particular model — IB rewards justification.
Frequently Asked Questions
Are arithmetic sequences ever correct in modelling?
Yes, but only when change is genuinely constant. IB expects students to justify this explicitly.
Why does IB prefer geometric sequences in finance and population?
Because they model percentage change, which reflects reality more accurately.
Can I lose marks even if my arithmetic sequence is correct?
Yes. If the model is inappropriate, correct calculations still lose marks. IB values reasoning over neat answers.
RevisionDojo Call to Action
Arithmetic sequences fail in modelling when realism is ignored. RevisionDojo helps IB Applications & Interpretation students choose models intelligently, justify assumptions, and explain limitations — exactly what examiners reward. If modelling questions feel unpredictable, RevisionDojo is the best place to build strong judgement skills.
