🔮 Algebra Realm · Sequences

Finding missing terms

Finding missing terms focuses on how to use surrounding terms and the sequence structure to fill gaps rather than guessing. In this lesson, focus on a sequence records values in order.

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Understand Finding missing terms

Finding missing terms focuses on how to use surrounding terms and the sequence structure to fill gaps rather than guessing. 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 finding missing terms, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Finding missing terms: A sequence records values in order. Use the rule to regenerate at least two terms already shown in the sequence. Keep the finding missing terms 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 finding missing terms.

Check as you go

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

Key vocabulary

termpositiondifferenceterm-to-term rulenth termfindingmissing

Rules and key facts

5, 8, __, 14 has missing term 11.

  • 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 finding missing terms.

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 finding missing terms.

What you need first

  • Recognise the vocabulary: term, position, difference.
  • Be able to explain the purpose of finding missing terms 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 finding missing terms.

Interactive maths model Connected to this topic; move controls, check outputs, then earn XP only from verified actions.
Responsive · validated · topic linked

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: Finding missing terms — Fill the gap: 3, 5, __, 9. Method choice: use the finding missing terms method and show each step with the stated values. Calculation or reasoning: The sequence increases by 2, so the missing term is 5 + 2 = 7. Final answer: 7. 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: Finding missing terms — Fill the gap: 3, 17, __, 45. Method choice: use the finding missing terms method and show each step with the stated values. Calculation or reasoning: The sequence increases by 14, so the missing term is 17 + 14 = 31. Final answer: 31. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check that every gap follows the same rule.

Challenge example

Stretch the idea

Given information: Finding missing terms — Fill the gap: 3, 16, __, 42. Method choice: use the finding missing terms method and show each step with the stated values. Calculation or reasoning: The sequence increases by 13, so the missing term is 16 + 13 = 29. Final answer: 29. 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: Finding missing terms — Fill the gap: 3, 15, __, 39. Method choice: use the finding missing terms method and show each step with the stated values. Calculation or reasoning: The sequence increases by 12, so the missing term is 15 + 12 = 27. Final answer: 27. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: Check the repaired sequence in both directions.

Common mistakes

  • Using a term-to-term rule as if it were an nth-term formula. This is a key trap when answering finding missing terms 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 finding missing terms answer.

Extension challenge

Create a finding missing terms problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

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Finding missing terms challenge

Use sequence machine controls to solve three checked finding missing terms rounds. Solve at least two of three marked rounds and use feedback to correct any error.

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Challenge Finding missing terms Arcane Boss

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Finding missing terms Arcane Boss

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Study cards

Core idea

Finding missing terms: A sequence records values in order. Use the rule to regenerate at least two terms already shown in the sequence. Keep the finding missing terms representation visible until the final line.

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Key vocabulary

term · position · difference · term-to-term rule · nth term · finding · missing

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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 finding missing terms.

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Formula / fact

5, 8, __, 14 has missing term 11.

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Foundation example

Given information: Finding missing terms — Fill the gap: 3, 5, __, 9. Method choice: use the finding missing terms method and show each step with the stated values. Calculation or reasoning: The sequence increases by 2, so the missing term is 5 + 2 = 7. Final answer: 7. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Finding missing terms — Fill the gap: 3, 17, __, 45. Method choice: use the finding missing terms method and show each step with the stated values. Calculation or reasoning: The sequence increases by 14, so the missing term is 17 + 14 = 31. Final answer: 31. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Finding missing terms — Fill the gap: 3, 16, __, 42. Method choice: use the finding missing terms method and show each step with the stated values. Calculation or reasoning: The sequence increases by 13, so the missing term is 16 + 13 = 29. Final answer: 29. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Finding missing terms — Fill the gap: 3, 15, __, 39. Method choice: use the finding missing terms method and show each step with the stated values. Calculation or reasoning: The sequence increases by 12, so the missing term is 15 + 12 = 27. Final answer: 27. 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 finding missing terms questions.

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Exam tip

For finding missing terms, 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 finding missing terms, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

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Help for Finding missing terms

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Simple explanation

Finding missing terms: A sequence records values in order. Use the rule to regenerate at least two terms already shown in the sequence. Keep the finding missing terms representation visible until the final line.

Think of finding missing terms 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 finding missing terms.

Hint 1

Start by naming the given information and the exact result required for finding missing terms.

Hint 2

List positions above the terms.

Full worked solution

Given information: Finding missing terms — Fill the gap: 3, 5, __, 9. Method choice: use the finding missing terms method and show each step with the stated values. Calculation or reasoning: The sequence increases by 2, so the missing term is 5 + 2 = 7. Final answer: 7. 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 finding missing terms.

Common mistake warning

Using a term-to-term rule as if it were an nth-term formula. This is a key trap when answering finding missing terms questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain finding missing terms 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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