Year 9 - Maths
Extrapolating a sequence
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 appreciate that there are other number sequences and the limitations of only seeing a few terms of a sequence.
Key Notes
- There are more sequences than the ones seen so far.
- A numerical sequence is just a set of numbers often following a rule.
- If you only see a few of the terms, it is possible to incorrectly deduce the rule.
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.
Common Mistakes To Avoid
- Sequences are either arithmetic or geometric.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There are more sequences than the ones seen so far. A numerical sequence is just a set of numbers often following a rule.
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: Sequences are either arithmetic or geometric. Correction: There are many ways sequences can be generated and you can usually find more than one rule than can fit the first few terms of a sequence. Exploring these will ensure pupils don't have a narrow experience of sequences.
More Lessons In This Unit
- Checking understanding of arithmetic sequences 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
- Recognising special number 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.