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generating sequences

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4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.

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Lesson Overview

Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA

Learning Objectives

Prerequisites

Materials & Equipment

Lesson 1: Introduction: generating sequences

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about generating sequences. Then check against the key terms: Sequence, Two types of rules. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Sequence, Two types of rules.
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: generating sequences. 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: Generate the first 5 terms starting at 2, adding 4 each time.

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about generating sequences.

Lesson 2: Core Concepts: generating sequences

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on generating sequences. Check them against the notes below.

Main Content (35 minutes)

Sequence: An ordered list of numbers. Each number is called a term.
Two types of rules: Term-to-term: How to get from one term to the next Position-to-term: Formula for the nth term

Practice (10 minutes)

Q: Generate the first 5 terms starting at 2, adding 4 each time.

Answer: 2, 6, 10, 14, 18

Plenary (5 minutes)

Explain Back

Your student teaches the key points back to you without looking. Fill any gaps immediately.

Lesson 3: Application: generating sequences

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: Sequence, Two types of rules. 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: Generate the first 5 terms starting at 2, adding 4 each time.

Answer: 2, 6, 10, 14, 18

Q2: Generate the first 4 terms starting at 1, multiplying by 2 each time.

Answer: 1, 2, 4, 8

Q3: Find the first 5 terms where uₙ = 3n - 1.

Answer: 2, 5, 8, 11, 14

Q4: Find the 15th term of uₙ = 2n + 5.

Answer: 35

Q5: Is 50 a term in the sequence uₙ = 6n + 2?

Answer: 6n + 2 = 50 → n = 8, so yes, 50 is the 8th term

Q6: Which term in the sequence uₙ = 7n - 4 equals 66?

Answer: n = 10 (the 10th term)

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: generating sequences

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 sequence has nth term 5n + 3. (a) Find the 1st, 10th and 100th terms. (b) Is 2023 in the sequence? Show working. (c) Two consecutive terms add to 73. Which two terms are they? <div class="

(a) 1st: 5(1) + 3 = 8. 10th: 5(10) + 3 = 53. 100th: 5(100) + 3 = 503 (b) 5n + 3 = 2023 → 5n = 2020 → n = 404. Yes, it's the 404th term. (c) Consecutive terms: (5n + 3) + (5(n+1) + 3) = 73 → 10n + 11 = 73 → 10n = 62 → n = 6.2. Not a whole number, so no two consecutive terms add to 73. Wait — let me recheck: 10n + 8 + 5 + 3 = 10n + 11. Hmm: (5n+3) + (5n+8) = 10n + 11 = 73 → n = 6.2. No integer solution. Actually this means 73 is not achievable. Mark scheme: (a) 2 marks. (b) 2 marks with working. (c) 2 marks for correct method and conclusion.

Exam Tips: Term-to-term: how to get from one term to the next | Position-to-term: formula using n for the nth term | n must be a whole number (positive integer) | To check if a number is in the sequence, solve for n | If n isn't a whole number, the term isn't in the sequence
Common Errors: Watch Out! 1. Wrong: Thinking the first term corresponds to n = 0 Correct: The first term always corresponds to n = 1 2. Wrong: Saying 50 is in the sequence 6n + 2 because 50 "looks right" Correct: Check algebraically: 6n + 2 = 50 → n = 8 (whole number), so yes it is the 8th term 3. Wrong: Confusing term-to-term with position-to-term rules Correct: Term-to-term tells how to get the next term; position-to-term gives a formula for any term directly
AO3 - Reasoning & Interpretation: Reasoning and Interpretation A savings account adds £15 per month. In month 1 the balance is £35. (a) Write a formula for the balance B in month n. (b) When does the balance exceed £500? (c) Explain why this model might not be realistic long-term. Answers: (a) B = 35 + 15(n - 1) = 15n + 20. (b) 15n + 20 > 500 → n > 32. So from month 33. (c) The model ignores interest earned and inflation; in reality savings grow with compound interest, not just linear deposits.
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how generating sequences connects to another Mathematics topic you have studied
  • Real-world: research one real-world use or example of generating sequences
  • Critical: "What are the limitations of the models used in generating sequences?"

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

Recommended Resources

🎓 Smart Lesson (Guided)