Recognising Sequences for IGCSE Maths

What You Need to Know

Identifying Fibonacci, triangular, cube, and other special sequences. This subtopic is part of Sequences in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding recognising sequences is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Recognising Sequences

Recognising the type of a sequence from its pattern is a Core and Extended skill. IGCSE 0580 tests four main types: linear (constant first difference, nth term = dn + c), quadratic (constant second difference, nth term has n²), geometric (constant ratio, nth term = arⁿ⁻¹), and other patterns such as triangular numbers (n(n+1)/2), square numbers (n²), cube numbers (n³), and Fibonacci-type sequences.

Step-by-Step Method

1. 1

   Calculate first differences

   Subtract consecutive terms. If first differences are constant → linear sequence.

2. 2

   Calculate second differences

   If first differences are not constant, subtract consecutive first differences. If second differences are constant → quadratic sequence.

3. 3

   Check for constant ratio

   Divide each term by the previous. If the ratio is constant → geometric sequence.

4. 4

   Recognise special sequences

   Triangular: 1, 3, 6, 10, 15 (differences increase by 1). Square: 1, 4, 9, 16. Fibonacci: each term is sum of two previous.

5. 5

   State the type and write the rule

   Name the sequence type and state how to find the next term.

Exam Tips for Recognising Sequences

• Always compute differences before ratios — linear and quadratic are more common than geometric in Paper 1.
• For 'continuing a pattern', identify the rule (difference or ratio) and apply it consistently.
• Triangular numbers 1,3,6,10,15 have nth term n(n+1)/2 — worth memorising as they appear regularly.
• A Fibonacci sequence has the rule: each term = sum of the two before it. The rule is NOT the nth term formula.

Practice Questions

Frequently Asked Questions