IGCSE Sequences and nth Term: Complete Guide for Cambridge IGCSE Mathematics

IGCSE sequences and nth term are essential algebra topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering arithmetic sequences, geometric sequences, and finding the nth term is essential for solving pattern problems.

This comprehensive IGCSE sequences and nth term guide covers everything you need to know, including identifying sequence types, finding nth term formulas, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to identify arithmetic and geometric sequences, find nth term formulas, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Sequences and nth Term Matter

IGCSE sequences and nth term are essential algebra topics. Here’s why they’re so important:

• High frequency topic: Sequence questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for understanding patterns and series
• Exam weight: Typically worth 4-7 marks per paper
• Real-world applications: Used in finance, computer science, and pattern recognition
• Problem-solving skills: Develops pattern recognition and algebraic thinking

Key insight from examiners: Students often confuse arithmetic and geometric sequences or make errors finding the nth term. This guide will help you master these systematically.

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Understanding Sequences

A sequence is an ordered list of numbers following a pattern.

Example: 2, 5, 8, 11, 14, ...

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Arithmetic Sequences

Arithmetic sequences have a constant difference between consecutive terms.

nth term formula: a_n = a + (n - 1)d

• a = first term
• d = common difference
• n = term number

Example 1: Find the nth term of 3, 7, 11, 15, ...

Solution: First term a = 3, common difference d = 4 a_n = 3 + (n - 1) × 4 = 3 + 4n - 4 = 4n - 1

Answer: a_n = 4n - 1

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Geometric Sequences

Geometric sequences have a constant ratio between consecutive terms.

nth term formula: a_n = ar^(n-1)

• a = first term
• r = common ratio
• n = term number

Example 2: Find the nth term of 2, 6, 18, 54, ...

Solution: First term a = 2, common ratio r = 3 a_n = 2 × 3^(n-1)

Answer: a_n = 2 × 3^(n-1)

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Finding Terms in Sequences

Example 3: For the sequence a_n = 5n + 2, find the 10th term.

Solution: a_10 = 5(10) + 2 = 50 + 2 = 52

Answer: 52

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Common Examiner Traps

• Confusing sequence types - Arithmetic has constant difference, geometric has constant ratio
• Formula errors - Remember (n-1) in formulas, not n
• Calculation errors - Double-check arithmetic

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Practice Questions

Question 1

Find the nth term of 5, 9, 13, 17, ...

Solution: Arithmetic sequence: a = 5, d = 4 a_n = 5 + (n - 1) × 4 = 4n + 1

Answer: a_n = 4n + 1

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Frequently Asked Questions About IGCSE Sequences and nth Term

What is a sequence?

A sequence is an ordered list of numbers following a pattern.

What is an arithmetic sequence?

An arithmetic sequence has a constant difference between consecutive terms.

What is a geometric sequence?

A geometric sequence has a constant ratio between consecutive terms.

How do I find the nth term?

Use the appropriate formula: a_n = a + (n-1)d for arithmetic, a_n = ar^(n-1) for geometric.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Linear Equations: Complete Guide - Master linear equations
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Sequences and nth Term with Tutopiya

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• Personalized 1-on-1 tutoring tailored to your learning pace
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Book a free IGCSE maths trial lesson and get personalized support to master sequences and achieve your target grade.

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