Year 11 - Maths
Introducing quadratic sequences
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 the features of a quadratic sequence.
Key Notes
- A quadratic sequence does not have a common difference.
- The second differences between terms are equal.
Vocabulary To Learn
- 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.
- Quadratic: A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2 When x is the variable, they have general form ax^2 + bx + c
Common Mistakes To Avoid
- Since there is no common difference, further terms in the sequence cannot be generated.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A quadratic sequence does not have a common difference. The second differences between terms are equal.
2. Use this key word in a maths sentence and explain it clearly. '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. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Since there is no common difference, further terms in the sequence cannot be generated. Correction: Pupils have seen sequences where the first difference is not common and seen examples of other rules. In this lesson, the concept of a second difference is introduced and this can be used to generate the next first difference.
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
- 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.