Year 9 - Maths
Securing understanding of arithmetic 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 begin to generalise a sequence.
Key Notes
- The n^th term is the generalised way of expressing any term in a sequence.
- For an arithmetic sequence, it will have the form d(n-1)+a
- The a refers to the first term of the sequence.
- The d refers to the common difference between any two consecutive terms.
Vocabulary To Learn
- Arithmetic/ linear sequence: An arithmetic (or linear) sequence is a sequence where the difference between successive terms is constant
Common Mistakes To Avoid
- Misinterpreting the values in an expression for the n^th term. For example, given the n^th term $$3n-5$$ pupils may think that this relates to a sequence that is decreasing by 5 each time
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The n^th term is the generalised way of expressing any term in a sequence. For an arithmetic sequence, it will have the form d(n-1)+a.
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: Misinterpreting the values in an expression for the n^th term. For example, given the n^th term $$3n-5$$ pupils may think that this relates to a sequence that is decreasing by 5 each time. Correction: Remind students about how the expression for the n^th term relates to multiples of a number (times tables) and then a shift. For example, 4, 9, 14, 19, ... can be seen as the 5 times table shifted down 1.
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
- Representing geometric sequences graphically Study Guide
Browse all guides in the Year 9 Maths guide library.