Year 9 - Maths
Recognising geometric 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 geometric sequence.
Key Notes
- Identifying a common ratio between each term can help us identify a geometric sequence.
- Divide each term by its previous consecutive term, if the results are all the same, this is the common ratio.
- If there is a common ratio, then the sequence is geometric.
Vocabulary To Learn
- Common ratio: A common ratio is a key feature of a geometric sequence. The constant multiplier between successive terms is called the common ratio.
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.
Identifying a common ratio between each term can help us identify a geometric sequence. Divide each term by its previous consecutive term, if the results are all the same, this is the common ratio.
2. Use this key word in a maths sentence and explain it clearly. 'Common ratio'
A common ratio is a key feature of a geometric sequence. The constant multiplier between successive terms is called the common ratio. 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 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.