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.
