Year 9 - Maths
Recognising special number sequences
Non-linear relationships
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit we explore geometric and special number sequences like the Fibonacci sequence. We develop strategies to recognise types of sequence and continue them.
Lesson Summary
You will learn to recognise a special number sequence.
Key Notes
- You can identify an arithmetic sequence by checking for a common difference between terms.
- You can identify a geometric sequence by checking for a common ratio between terms.
- You can identify a special number sequence if you can identify how to generate the sequence.
Vocabulary To Learn
- Arithmetic/linear sequence: An arithmetic (or linear) sequence is a sequence where the difference between successive terms is constant.
- Geometric sequence: A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.
- Triangular: A triangular number is a number that can be represented by a pattern of dots arranged into an equilateral triangle. The term number is the number of dots in a side of the triangle
Common Mistakes To Avoid
- After becoming very familiar with arithmetic sequences pupils can find the difference between the first two terms and just assume the sequence is arithmetic.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
You can identify an arithmetic sequence by checking for a common difference between terms. You can identify a geometric sequence by checking for a common ratio between terms.
2. Use this key word in a maths sentence and explain it clearly. 'Arithmetic/linear sequence'
An arithmetic (or linear) sequence is a sequence where the difference between successive terms is constant. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: After becoming very familiar with arithmetic sequences pupils can find the difference between the first two terms and just assume the sequence is arithmetic. Correction: Explore a large number of geometric and arithmetic sequences and see if pupils can articulate how they check if a sequence is geometric. They might say the terms of the sequence grow more quickly (for some geometric sequences).
More Lessons In This Unit
- Checking understanding of arithmetic sequences Study Guide
- Extrapolating a sequence Study Guide
- Features of geometric sequences Study Guide
- Features of special number sequences Study Guide
- Graphing special number sequences using technology Study Guide
- Problem solving with non-linear relationships Study Guide
- Recognising geometric sequences Study Guide
- Representing geometric sequences graphically Study Guide
- Securing understanding of arithmetic sequences Study Guide
Browse all guides in the Year 9 Maths guide library.