Year 11 - Maths
Reasoning about values in an arithmetic sequence
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 reason whether a value appears in a given sequence.
Key Notes
- It is possible to generate the sequence and therefore show whether a value appears in the sequence.
- It is possible to use your knowledge of multiples to reason whether a value appears in a given sequence.
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 nth term of a sequence is the position of a term in a sequence where n stands for the term number.
Common Mistakes To Avoid
- As long as the equation can be solved, the value will be in the sequence.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
It is possible to generate the sequence and therefore show whether a value appears in the sequence. It is possible to use your knowledge of multiples to reason whether a value appears in a given sequence.
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: As long as the equation can be solved, the value will be in the sequence. Correction: For the value to be in the sequence, the value for $$n$$ must be a positive integer. If it is not, then the value is not in the sequence as the term number must be a positive integer.
More Lessons In This Unit
- Advanced problem solving with further sequences Study Guide
- Arithmetic sequences and their graphs 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
- Sequence notation Study Guide
Browse all guides in the Year 11 Maths guide library.