Sequences
Sequence questions test pattern recognition and formula derivation. Students work with arithmetic, geometric, quadratic and special sequences, finding nth-term rules and using them to solve problems.
What You'll Learn
- Finding the nth term of an arithmetic (linear) sequence
- Finding the nth term of a quadratic sequence
- Recognising and continuing geometric sequences
- Identifying special sequences (triangular, Fibonacci, square numbers)
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Confusing the common difference with the first term when writing the nth-term formula
Using the term-to-term rule instead of the position-to-term rule for the nth term
Making arithmetic errors with negative common differences
What Examiners Say About Sequences
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Misconception●●●●●
You can ONLY cancel FACTORS (things multiplied), not terms added/subtracted. Factorise numerator and denominator first, then cancel matching brackets. Never cancel x² from x² − 25.
Source: CIE 0580 · May/June 2021 · Paper 4 · Q7a
- Presentation●●●●●
In 'show that k = 8' questions, you must DERIVE 8, not assume it. Starting from 'k = 8' and working both ways is circular and scores zero. Work from the given info towards the target.
Source: CIE 0580 · May/June 2021 · Paper 3 · Q5
- Common Mistake●●●●●
When raising a power to a power, MULTIPLY the exponents: (x³)³ = x⁹, not x⁶. But for coefficients like (4x³)³, the coefficient is raised: 4³ = 64, not 4 × 3 = 12.
Source: CIE 0580 · Feb/March 2024 · Paper 2 · Q21b
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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Related Topics
Graphing Linear Equations
Straight-line graphs form the basis for understanding gradients, intercepts and real-world modelling. Students need to plot lines from equations, find gradients and interpret y = mx + c.
Quadratic Graphs
Quadratic graphs produce a characteristic U-shape (parabola). Students must plot quadratics from tables, identify key features like turning points and roots, and use graphs to solve equations.
Functions
Function notation formalises the input-output relationship. Students evaluate, combine, and find inverses of functions, building skills that are directly extended in further study.
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