Year 11 - Maths
Checking and securing rules for generating arithmetic 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 identify the term-to-term rule and the position-to-term rule and express the latter algebraically.
Key Notes
- The term-to-term rule is the common difference.
- Finding the common difference can help when finding the n^th term rule.
- Comparing the sequence to an appropriate multiplication table can help identify the translation that has been made.
- The n^th term can be found for all arithmetic sequences.
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
- Arithmetic sequences only have a positive integer as the common difference.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The term-to-term rule is the common difference. Finding the common difference can help when finding the n^th term rule.
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: Arithmetic sequences only have a positive integer as the common difference. Correction: Arithmetic sequences can be increasing or decreasing and can have any value for the common difference.
More Lessons In This Unit
- Advanced problem solving with further sequences Study Guide
- Arithmetic sequences and their graphs 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.