Year 9 - Maths
Representing geometric sequences graphically
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 represent geometric sequences graphically and appreciate the common structure.
Key Notes
- A geometric sequence looks like a curve when sketched (common ratio > 1 or < 1).
- The gradient increases sharply (common ratio > 1 or < 1).
- Although the graph is continuous, the sequence is not.
- Each geometric sequence is made up of discrete terms.
Vocabulary To Learn
- Geometric sequence: A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.
- 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
- Pupils may thing that given the graph is continuous, the sequence can contain all of the values represented by the line.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A geometric sequence looks like a curve when sketched (common ratio > 1 or < 1). The gradient increases sharply (common ratio > 1 or < 1).
2. Use this key word in a maths sentence and explain it clearly. 'Geometric sequence'
A geometric sequence is a sequence with a constant multiplicative relationship between successive terms. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may thing that given the graph is continuous, the sequence can contain all of the values represented by the line. Correction: It is important that pupils know when it is appropriate to draw a line to graph sequences and whether values on the line have any meaning. Sequences are often given as a list of terms and without context we cannot assume the sequence is continuous.
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
- Recognising special number sequences Study Guide
- Securing understanding of arithmetic sequences Study Guide
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