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Auralith Learning

Year 7 · Maths · Sequences · Lesson 2

Term-to-term rules and patterns

Generate sequences from a first term and a term-to-term rule, including two-step rules, and solve pattern problems.

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

27-minute video lesson

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

Watch free for a month

What your child will learn

  • Generate a sequence from a rule
  • Use two-step term-to-term rules
  • Solve problems with patterns
  • Work backwards to find earlier terms
  • Compare two sequences

The method

  1. Write the first term.
  2. Apply the rule to get the next term.
  3. Always apply the rule to the term before.
  4. To work backwards, use the opposite operation.

Key words: term-to-term rule, first term, sequence, pattern, operation.

Worked examples

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

Question 1

The first term of a sequence is 6. The rule is 'add 5'. Write the first 5 terms.

  1. Step 1: 1st term: 6
  2. Step 2: 6 + 5 = 11
  3. Step 3: 11 + 5 = 16
  4. Step 4: 16 + 5 = 21
  5. Step 5: 21 + 5 = 26

Answer: 6, 11, 16, 21, 26

Question 2

The first term of a sequence is 1. The rule is 'add 9'. Write the first 5 terms.

  1. Step 1: 1st term: 1
  2. Step 2: 1 + 9 = 10
  3. Step 3: 10 + 9 = 19
  4. Step 4: 19 + 9 = 28
  5. Step 5: 28 + 9 = 37

Answer: 1, 10, 19, 28, 37

Question 3

The first term of a sequence is 50. The rule is 'subtract 8'. Write the first 5 terms.

  1. Step 1: 1st term: 50
  2. Step 2: 50 − 8 = 42
  3. Step 3: 42 − 8 = 34
  4. Step 4: 34 − 8 = 26
  5. Step 5: 26 − 8 = 18

Answer: 50, 42, 34, 26, 18