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Auralith Learning

Year 8 · Maths · Sequences and the nth term · Lesson 1

Term-to-term and nth term rules

Continue sequences, find missing terms, use term-to-term rules, and generate terms from an nth term formula.

Whiteboard video lesson: Term-to-term and nth term rules

26-minute video lesson

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

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What your child will learn

  • Continue a sequence using the term-to-term rule
  • Find missing terms
  • Recognise linear sequences
  • Generate a sequence from an nth term
  • Find any term from the nth term

The method

  1. Find the difference between terms.
  2. Same difference each time: linear sequence.
  3. nth term: substitute n = 1, 2, 3, ...
  4. For the 10th term, substitute n = 10.

Key words: sequence, term, term-to-term rule, nth term, linear.

Worked examples

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

Question 1

Write the next 2 terms of the sequence 5, 9, 13, 17, ...

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

Answer: 21, 25

Question 2

Write the next 2 terms of the sequence 2, 8, 14, 20, ...

  1. Step 1: Find the differences
  2. Step 2: Rule: add 6 each time
  3. Step 3: Continue the sequence

Answer: 26, 32

Question 3

Write the next 2 terms of the sequence 30, 26, 22, 18, ...

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

Answer: 14, 10