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Year 6 · Maths · Algebra and sequences · Lesson 1

Linear sequences

Continue linear sequences including negatives and fractions, fill missing terms, generate sequences from rules, and find terms further along.

Whiteboard video lesson: Linear sequences

20-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Find term-to-term rules
  • Continue sequences
  • Find missing terms
  • Generate sequences from a rule
  • Find a term far along a sequence

The method

  1. Find the difference.
  2. Write the rule.
  3. Continue or fill gaps.
  4. Far terms: first + jumps × difference.

Key words: sequence, term, rule, difference, linear.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Write the next 2 terms of the sequence 2, 6, 10, 14, ...

  1. Step 1: Find the differences
  2. Step 2: Rule: add 4 each time
  3. Step 3: Continue the sequence

Answer: 18, 22

Question 2

Write the next 2 terms of the sequence 5, 12, 19, 26, ...

  1. Step 1: Find the differences
  2. Step 2: Rule: add 7 each time
  3. Step 3: Continue the sequence

Answer: 33, 40

Question 3

Write the next 2 terms of the sequence 40, 35, 30, 25, ...

  1. Step 1: Find the differences
  2. Step 2: Rule: subtract 5 each time
  3. Step 3: Continue the sequence

Answer: 20, 15