Year 8 - Maths
Finding the nth term
Sequences
Study Hub
Study Guides
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 find the n^th term rule by investigating the common difference.
Key Notes
- 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.
- The n^th term rule can be used to identify the term number of a given number in a sequence.
Vocabulary To Learn
- 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
- That the sequence 6,11,16,21, ... is 5n+6 because it goes up by 5 and starts at 6.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
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.
2. Use this key word in a maths sentence and explain it clearly. '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. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: That the sequence 6,11,16,21, ... is 5n+6 because it goes up by 5 and starts at 6. Correction: Compare 6,11,16,21, ... to 5,10,15,20, ... "What is the shift? The translation? If that is 5n then this is 5n with how much more?".
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
- Formalising a sequence Study Guide
- Generating a sequence using a position-to-term rule Study Guide
- Generating a sequence using a term-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
Browse all guides in the Year 8 Maths guide library.