nth term
4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.
Lesson Overview
Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA
Learning Objectives
- Explain the key ideas of nth term
- Apply nth term to exam-style questions
- Develop independent study skills
- Build cross-topic connections
Prerequisites
- Read the revision notes for nth term first (GCSE Revise summary)
- Key vocab to pre-teach: nth term, Position numbers
- Basic skills: reading the summary notes and answering the practice questions there
Materials & Equipment
- Exercise book, pencil, ruler
- Scientific calculator
- Pair of compasses and protractor (geometry topics)
- Graph paper
- Printed revision notes (link below)
Lesson 1: Introduction: nth term
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Write down everything you already know about nth term. Then check against the key terms: nth term, Position numbers. Use a mini-whiteboard or paper.
Main Content (35 minutes)
Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: nth term, Position numbers.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Before lesson: Read the script below. Pre-teach key vocab: nth term, Position numbers.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: nth term. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Mathematics because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
Mins 0-5 - Hook: "Today: nth term. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Mathematics because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
First Look
Start with the revision notes summary, then attempt: Find the nth term of: 6, 10, 14, 18, 22, ...
Plenary (5 minutes)
Check Out
Your student states one thing they learned and one question they still have about nth term.
Lesson 2: Core Concepts: nth term
Duration: 50 minutes
Starter Activity (5 minutes)
Review Previous Lesson
Quick recap: write 3 key points from Lesson 1 on nth term. Check them against the notes below.
Main Content (35 minutes)
nth term: A formula that allows you to find any term in a sequence without working out all the previous terms.
Position numbers: The position of each term (1st = position 1, 2nd = position 2, etc.)
Practice (10 minutes)
Q: Find the nth term of: 6, 10, 14, 18, 22, ...
Answer: 4n + 2
Plenary (5 minutes)
Explain Back
Your student teaches the key points back to you without looking. Fill any gaps immediately.
Lesson 3: Application: nth term
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Recall the key terms: nth term, Position numbers. Define each in one sentence.
Main Content (35 minutes)
Parent/Teacher Guide: Let your student attempt each question alone first, then compare with the model answer. Award method marks for correct working even if the final answer is wrong.
Q1: Find the nth term of: 6, 10, 14, 18, 22, ...
Answer: 4n + 2
Q2: Find the nth term of: 50, 46, 42, 38, 34, ...
Answer: -4n + 54 or 54 - 4n
Q3: Find the 100th term of: 7n - 3
Answer: 697
Q4: Is 80 a term in the sequence 5n + 10?
Answer: 5n + 10 = 80 → n = 14, yes it's the 14th term
Q5: Find the nth term of: 2, 5, 10, 17, 26, ...
Answer: n² + 1
Q6: Find the nth term of: 6, 11, 18, 27, 38, ...
Answer: n² + 2n + 3
Plenary (5 minutes)
Error Review
Review any questions answered incorrectly. Identify whether the error was knowledge, method, or reading the question.
Lesson 4: Exam Practice: nth term
Duration: 50 minutes
Starter Activity (5 minutes)
Command Words
Review what these command words require: state (one point), describe (say what happens), explain (say why), compare (both sides), evaluate (judgement).
Main Content (35 minutes)
Extended Answer
Extended question: Extended Answer 6 marks: A pattern uses tiles: 7, 11, 17, 25, 35, ... (a) Show this is a quadratic sequence. (b) Find the nth term. (c) How many tiles are needed for the 20th pattern? (d) Is 200 tiles possible? <div class="
(a) 1st diff: 4, 6, 8, 10. 2nd diff: 2, 2, 2. Constant second difference = quadratic. (b) Half of 2nd diff = 1, so n². n²: 1, 4, 9, 16, 25. Remainder: 6, 7, 8, 9, 10. This is n + 5. So nth term = n² + n + 5 (c) 20² + 20 + 5 = 400 + 20 + 5 = 425 tiles (d) n² + n + 5 = 200 → n² + n - 195 = 0 → n = (-1 + √(1+780))/2 = (-1 + √781)/2 ≈ (-1 + 27.95)/2 ≈ 13.47. Not a whole number, so 200 is not possible. Mark scheme: (a) 1 mark. (b) 2 marks. (c) 1 mark. (d) 2 marks for solving and conclusion.
Exam Tips: Linear: Find difference, then multiply n by this and adjust | Quadratic: Check second difference are constant | Half of second difference = coefficient of n² | Always check by substituting n = 1, 2, 3 | For linear, quick check: 1st term shows if constant is right
Common Errors: Watch Out! 1. Wrong: For a decreasing sequence like 20, 17, 14, ... the nth term is 3n + 17 Correct: Difference is -3, so nth term is -3n + 23 (check: n=1 gives 20 ✓) 2. Wrong: For quadratic sequences, using the first difference as the coefficient of n² Correct: Use HALF of the SECOND difference as the coefficient of n² 3. Wrong: Saying 100 is in the sequence 3n - 1 because it "looks about right" Correct: Check: 3n - 1 = 100 → n = 33.67 (not integer). 100 is NOT in the sequence.
AO3 - Reasoning & Interpretation: Reasoning and Interpretation The number of seats in each row of a theatre follows a pattern: 20, 24, 30, 38, 48, ... (a) Find the nth term. (b) There are 25 rows. How many seats in the last row? (c) The fire limit is 60 seats per row. Are any rows over the limit? Answers: (a) 1st diff: 4, 6, 8, 10. 2nd diff: 2. Half = 1, so n². n²: 1, 4, 9, 16, 25. Remainder: 19, 20, 21, 22, 23 = n + 18. nth term = n² + n + 18. (b) Row 25: 625 + 25 + 18 = 668 seats. (c) Yes — from row 7 onwards (7² + 7 + 18 = 74 > 60). The theatre would need safety adjustments.
Stretch & Challenge (Grade 8-9):
- Synoptic links: explain how nth term connects to another Mathematics topic you have studied
- Real-world: research one real-world use or example of nth term
- Critical: "What are the limitations of the models used in nth term?"
Plenary (5 minutes)
Assessment Criteria
- Got it: Confident explanation + correct worked examples
- Getting there: Main points OK, needs support with detail
- Not yet: Confused on key concepts - re-run Lesson 2
Homework & Consolidation
- Consolidation: Re-answer any Lesson 3 practice questions answered incorrectly (20 mins)
- Retrieval: Write flashcards for the key terms: nth term, Position numbers (10 mins)
- Exam practice: One past-paper question on nth term from the board websites (15 mins)
- Extension: Explain nth term to someone else in your own words (10 mins)