Sequences & the nth Term
Find the nth term rule of a linear sequence and use it to generate terms and check membership.
Overview
A sequence is a list of numbers that follow a rule. In Year 9 students move from term-to-term rules to position-to-term rules — finding the nth term of a linear sequence, such as 3n + 1. The nth term lets you find any term instantly and check whether a number belongs to the sequence. It is a key IGCSE algebra skill.
What You Will Learn
- Continue a linear sequence and describe its term-to-term rule
- Find the nth term rule of a linear sequence
- Use the nth term to generate any term of a sequence
- Check whether a given number is a term of a sequence
- Recognise simple non-linear sequences such as square numbers
Key Vocabulary
Common Mistakes to Avoid
- Using the term-to-term rule when asked for the nth term (position-to-term) rule
- Forgetting the constant — giving 3n instead of 3n + 1
- Getting the sign of the common difference wrong in a decreasing sequence
- Substituting the term value instead of the position number into the nth term
What Comes Next
At IGCSE this extends to the nth term of quadratic sequences and to other special sequences, within the Algebra and Graphs topic.
Frequently Asked Questions
How do I find the nth term of a linear sequence?
Find the common difference between terms — that is the number in front of n. Then work out what to add or subtract to get the first term. For 4, 7, 10, 13, the difference is 3, so it starts with 3n; 3×1 = 3, and we need 4, so add 1: the nth term is 3n + 1.
What is the difference between term-to-term and nth term rules?
A term-to-term rule tells you how to get from one term to the next (e.g. 'add 3'). The nth term (position-to-term) rule lets you find any term directly from its position, without listing all the terms before it.
Study This Topic
Topic Details
- Stage
- Year 9
- Strand
- Algebra
- Framework ref
- 9As
- Difficulty
- High
Build strong foundations in Sequences & the nth Term
A free trial class with Teacher Rig helps your Year 9 child master Sequences & the nth Term now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Sequences & the nth Term develops in IGCSE Algebra and Graphs (Cambridge 0580) →