Year 11 - Maths
Arithmetic sequences and their graphs
Further sequences
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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, pupils consider different types of sequences such as Fibonacci and oscillating sequences. They then consolidate their knowledge of different types of sequences by solving contextual problems.
Lesson Summary
You will learn to recognise that an arithmetic sequence can be shown graphically and how this relates to the equation of a linear graph and use this to find the n^th term formula.
Key Notes
- The n^th term rule can be generated from the sequence.
- The n^th term rule can be generated from the graph.
- The n^th term rule is the equation of the line.
Vocabulary To Learn
- Arithmetic sequence: An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.
- n^th term: The n^th term of a sequence is the position of a term in a sequence where n stands for the term number.
Common Mistakes To Avoid
- When plotting a sequence you should always connect the points with a line.
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 rule can be generated from the sequence. The n^th term rule can be generated from the graph.
2. Use this key word in a maths sentence and explain it clearly. 'Arithmetic sequence'
An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When plotting a sequence you should always connect the points with a line. Correction: Only the (term number, term value) should be plotted. Points should not be joined as these are discrete values.
More Lessons In This Unit
- Advanced problem solving with further sequences Study Guide
- Checking and securing rules for generating arithmetic sequences Study Guide
- Checking and securing understanding of geometric sequences Study Guide
- Checking and securing understanding of special number sequences Study Guide
- Conditions in arithmetic sequences Study Guide
- Fibonacci and alternating sequences Study Guide
- Identifying values in an arithmetic sequence Study Guide
- Introducing quadratic sequences Study Guide
- Problem solving with further sequences Study Guide
- Quadratic sequences Study Guide
- Reasoning about values in an arithmetic sequence Study Guide
- Sequence notation Study Guide
Browse all guides in the Year 11 Maths guide library.