Sequences Revision Notes for IGCSE Maths
These comprehensive revision notes cover everything you need to know about sequences for the Cambridge IGCSE Mathematics 0580 examination. Written by Teacher Rig, each section includes key concepts, essential formulas, and practical exam tips to help you achieve your best grade.
Linear (Arithmetic) Sequences
A linear sequence has a constant difference between consecutive terms. The nth term is an + b where a is the common difference and b = first term - a. The general term can also be written as a + (n-1)d where a is the first term and d is the common difference.
Key Formulas
- nth term = dn + (first term - d)
- nth term = a + (n-1)d
- Common difference d = second term - first term
Exam Tips
- Always verify your formula works for n = 1, 2, and 3
- The common difference d is the coefficient of n
- If the sequence decreases, d is negative
Quadratic Sequences
A quadratic sequence has a constant second difference. The nth term is an squared + bn + c. To find a: a = second difference / 2. Then subtract an squared from each term to get a linear sequence, which gives bn + c.
Key Formulas
- Second difference = 2a
- nth term = an squared + bn + c
Exam Tips
- Always check first differences first - if they are constant, it is linear, not quadratic
- After finding the an squared part, the remaining terms should form a linear sequence
- Some quadratic sequences can be spotted as perfect squares or other patterns
Geometric Sequences
A geometric sequence has a constant ratio between consecutive terms. Each term is found by multiplying the previous term by the common ratio r. The nth term is ar^(n-1) where a is the first term.
Key Formulas
- nth term = ar^(n-1)
- Common ratio r = second term / first term
- Sum of n terms = a(1 - r^n) / (1 - r)
Exam Tips
- The common ratio can be negative (terms alternate in sign)
- If |r| < 1, the terms get smaller
- Check: multiply any term by r to get the next term
Sum of Arithmetic Series
The sum of the first n terms of an arithmetic sequence can be found using a formula. This is useful for finding the total of many terms without adding them individually.
Key Formulas
- S(n) = n/2 (2a + (n-1)d)
- S(n) = n/2 (a + l) where l is the last term
Exam Tips
- The second formula is easier if you know the last term
- Both formulas give the same result
- Remember Gauss's trick: pair first and last terms
Revision Checklist
- I understand all key concepts in sequences
- I have memorised the essential sequences formulas
- I can apply these concepts to exam-style questions
- I have practised past paper questions on sequences
- I know the common mistakes to avoid in sequences questions
Frequently Asked Questions
What sequences topics are covered in IGCSE Maths?
The IGCSE 0580 syllabus covers sequences across both Core and Extended tiers. Key areas include linear (arithmetic) sequences. Key areas include quadratic sequences. Key areas include geometric sequences.
How important is sequences in the IGCSE exam?
Sequences is a significant part of the IGCSE Mathematics exam, typically appearing in Paper 2 (non-calculator) and Paper 4 (calculator). Questions range from straightforward calculations to multi-step problems that combine sequences with other topics.
What are the most common mistakes in sequences?
Common mistakes include not showing full working, forgetting to state units, misreading the question, and rushing through calculations. For sequences specifically, make sure you understand the underlying concepts rather than just memorising procedures.
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