🔮 Algebra Realm · Sequences

Continuing diagram sequences

Continuing diagram sequences focuses on how to extend visual patterns by identifying exactly what is added at each diagram stage. In this lesson, focus on a sequence records values in order.

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Understand Continuing diagram sequences

Continuing diagram sequences focuses on how to extend visual patterns by identifying exactly what is added at each diagram stage. In this lesson, focus on a sequence records values in order.

A sequence records values in order. A term-to-term rule explains the move from one term to the next, while the positions keep the order visible. For continuing diagram sequences, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Continuing diagram sequences: A sequence records values in order. Use the rule to regenerate at least two terms already shown in the sequence. Keep the continuing diagram sequences representation visible until the final line.

Picture the idea

Run terms through a sequence machine and compare a step-by-step growth view with a position-to-term table. Use the model to explain one change you notice while working on continuing diagram sequences.

Check as you go

Use the rule to regenerate at least two terms already shown in the sequence. Write that check beside the final continuing diagram sequences answer.

Key vocabulary

termpositiondifferenceterm-to-term rulenth termcontinuingdiagram

Rules and key facts

A row of 3, 5, 7 dots gains 2 dots, so stage four has 9.

  • List positions above the terms.
  • Inspect the change pattern or substitute the required position.
  • Apply the rule carefully to the requested term.
  • Check against known terms before extending the pattern. Record the check explicitly for continuing diagram sequences.

Step-by-step method

  1. List positions above the terms.
  2. Inspect the change pattern or substitute the required position.
  3. Apply the rule carefully to the requested term.
  4. Check against known terms before extending the pattern. Record the check explicitly for continuing diagram sequences.

What you need first

  • Recognise the vocabulary: term, position, difference.
  • Be able to explain the purpose of continuing diagram sequences before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Tile patterns
  • Predicting repeated growth

Visual / interactive

See the idea, then move it around

Skip to Practice

Run terms through a sequence machine and compare a step-by-step growth view with a position-to-term table. Use the model to explain one change you notice while working on continuing diagram sequences.

Interactive maths model Connected to this topic; move controls, check outputs, then earn XP only from verified actions.
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Worked examples

Examples, methods and exam thinking

Level 1 · Foundation

Understand the idea with small numbers, one representation and one clear step.

Level 2 · Secure

Use the standard Year 8 method with mixed examples and normal wording.

Level 3 · Challenge

Handle multi-step or less familiar questions and explain choices.

Level 4 · Exam-style

Solve a worded question, show reasoning, check accuracy and write a final sentence.

Foundation example

Build confidence

Given information: Continuing diagram sequences — The sequence starts 3, 5, 7. Find the next term. Method choice: use the continuing diagram sequences method and show each step with the stated values. Calculation or reasoning: The common difference is 2. Add 2 once more: 7 + 2 = 9. Final answer: 9. Check: substitute or compare with the original information to confirm the result fits the question.

  1. List positions above the terms.
  2. Inspect the change pattern or substitute the required position.
  3. Apply the rule carefully to the requested term.
Secure example

Use the normal method

Given information: Continuing diagram sequences — The sequence starts 3, 17, 31. Find the next term. Method choice: use the continuing diagram sequences method and show each step with the stated values. Calculation or reasoning: The common difference is 14. Add 14 once more: 31 + 14 = 45. Final answer: 45. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Draw the next stage and confirm its total.

Challenge example

Stretch the idea

Given information: Continuing diagram sequences — The sequence starts 3, 16, 29. Find the next term. Method choice: use the continuing diagram sequences method and show each step with the stated values. Calculation or reasoning: The common difference is 13. Add 13 once more: 29 + 13 = 42. Final answer: 42. Check: substitute or compare with the original information to confirm the result fits the question.

Try explaining why each step works before checking the answer.

Exam-style example

Show your reasoning

Given information: Continuing diagram sequences — The sequence starts 3, 15, 27. Find the next term. Method choice: use the continuing diagram sequences method and show each step with the stated values. Calculation or reasoning: The common difference is 12. Add 12 once more: 27 + 12 = 39. Final answer: 39. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: Annotate the added piece, not only the totals.

Common mistakes

  • Using a term-to-term rule as if it were an nth-term formula. This is a key trap when answering continuing diagram sequences questions.
  • Starting position counting at zero without being told.

How to check your answer

Use the rule to regenerate at least two terms already shown in the sequence. Write that check beside the final continuing diagram sequences answer.

Extension challenge

Create a continuing diagram sequences problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

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Continuing diagram sequences challenge

Use sequence machine controls to solve three checked continuing diagram sequences rounds. Solve at least two of three marked rounds and use feedback to correct any error.

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Study cards

Core idea

Continuing diagram sequences: A sequence records values in order. Use the rule to regenerate at least two terms already shown in the sequence. Keep the continuing diagram sequences representation visible until the final line.

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Key vocabulary

term · position · difference · term-to-term rule · nth term · continuing · diagram

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Rules

List positions above the terms. Inspect the change pattern or substitute the required position. Apply the rule carefully to the requested term. Check against known terms before extending the pattern. Record the check explicitly for continuing diagram sequences.

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Formula / fact

A row of 3, 5, 7 dots gains 2 dots, so stage four has 9.

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Foundation example

Given information: Continuing diagram sequences — The sequence starts 3, 5, 7. Find the next term. Method choice: use the continuing diagram sequences method and show each step with the stated values. Calculation or reasoning: The common difference is 2. Add 2 once more: 7 + 2 = 9. Final answer: 9. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Continuing diagram sequences — The sequence starts 3, 17, 31. Find the next term. Method choice: use the continuing diagram sequences method and show each step with the stated values. Calculation or reasoning: The common difference is 14. Add 14 once more: 31 + 14 = 45. Final answer: 45. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Continuing diagram sequences — The sequence starts 3, 16, 29. Find the next term. Method choice: use the continuing diagram sequences method and show each step with the stated values. Calculation or reasoning: The common difference is 13. Add 13 once more: 29 + 13 = 42. Final answer: 42. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Continuing diagram sequences — The sequence starts 3, 15, 27. Find the next term. Method choice: use the continuing diagram sequences method and show each step with the stated values. Calculation or reasoning: The common difference is 12. Add 12 once more: 27 + 12 = 39. Final answer: 39. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Using a term-to-term rule as if it were an nth-term formula. This is a key trap when answering continuing diagram sequences questions.

Tap to mark reviewed
Exam tip

For continuing diagram sequences, show the key representation before the final calculation. Use this final check: Use the rule to regenerate at least two terms already shown in the sequence.

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Real-world use

Tile patterns, Predicting repeated growth

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Checklist

I can explain continuing diagram sequences, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

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Help for Continuing diagram sequences

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Simple explanation

Continuing diagram sequences: A sequence records values in order. Use the rule to regenerate at least two terms already shown in the sequence. Keep the continuing diagram sequences representation visible until the final line.

Think of continuing diagram sequences as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.

Step-by-step breakdown

  1. List positions above the terms.
  2. Inspect the change pattern or substitute the required position.
  3. Apply the rule carefully to the requested term.
  4. Check against known terms before extending the pattern. Record the check explicitly for continuing diagram sequences.

Hint 1

Start by naming the given information and the exact result required for continuing diagram sequences.

Hint 2

List positions above the terms.

Full worked solution

Given information: Continuing diagram sequences — The sequence starts 3, 5, 7. Find the next term. Method choice: use the continuing diagram sequences method and show each step with the stated values. Calculation or reasoning: The common difference is 2. Add 2 once more: 7 + 2 = 9. Final answer: 9. Check: substitute or compare with the original information to confirm the result fits the question.

Method: List positions above the terms. → Inspect the change pattern or substitute the required position. → Apply the rule carefully to the requested term. → Check against known terms before extending the pattern. Record the check explicitly for continuing diagram sequences.

Common mistake warning

Using a term-to-term rule as if it were an nth-term formula. This is a key trap when answering continuing diagram sequences questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain continuing diagram sequences in my own words.
  • I can use these words accurately: term, position, difference.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Using a term-to-term rule as if it were an nth-term formula.
  • I can apply this check: Use the rule to regenerate at least two terms already shown in the sequence.
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