Year 8 - Maths
Generating a sequence using a term-to-term rule
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 we develop knowledge of sequences to be able to identify, determine, and continue arithmetic sequences. We finish the unit by looking at how sequences may be reprsented graphically.
Lesson Summary
You will learn to appreciate that a sequence can be generated and described using term-to-term approaches.
Key Notes
- Sequences can be created using a rule that tells you how to find the next term from the current one.
- These sequences could be related additively or multiplicity.
- These sequences could be related in other ways.
- This term-to-term method is time-consuming when you want to find higher terms in the sequence.
- It is possible to describe the rule when given some of the terms although this may not be unique.
Vocabulary To Learn
- Term-to-term: A term-to-term rule describes how to calculate the next term in the sequence from the previous term.
Common Mistakes To Avoid
- The difference in the given terms divided by the number of missing terms gives the common difference
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Sequences can be created using a rule that tells you how to find the next term from the current one. These sequences could be related additively or multiplicity.
2. Use this key word in a maths sentence and explain it clearly. 'Term-to-term'
A term-to-term rule describes how to calculate the next term in the sequence from the previous term. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: The difference in the given terms divided by the number of missing terms gives the common difference. Correction: Write the sequence out with gaps for the missing terms. Model how many additions (jumps) to get from one known term to the next.
More Lessons In This Unit
- Arithmetic sequences Study Guide
- Calculating any term Study Guide
- Checking understanding of sequences Study Guide
- Expressing an arithmetic sequence Study Guide
- Finding the nth term Study Guide
- Formalising a sequence Study Guide
- Generating a sequence using a position-to-term rule Study Guide
- Justifying terms of a sequence Study Guide
- Problem solving with sequences Study Guide
- Representing sequences graphically Study Guide
- Securing understanding of sequences Study Guide
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