Number Patterns • Topic 1 of 3

Growing Patterns

A pattern is a sequence that follows a rule. In a growing pattern, each term is larger than the one before it.

  • Add patterns: 5, 10, 15, 20, 25 — Rule: +5 each time
  • Multiply patterns: 2, 4, 8, 16, 32 — Rule: ×2 each time

To find the rule: check what you add or multiply to get from one term to the next. Then use that rule to find the missing term.

Steps to extend a growing pattern:

  1. Look at two consecutive terms
  2. Find the difference (for add) or ratio (for multiply)
  3. Check it works for the next pair too
  4. Apply the rule to find the next term
Growing Patterns2→4→8→16→32x2x2x2x2Rule: x2 (multiply by 2 each time)
Solved Examples
1
Worked Example
Find the next two terms: 3, 6, 9, 12, ___, ___
SolutionStep 1: 6 - 3 = 3, 9 - 6 = 3, 12 - 9 = 3. Rule = +3 each time. Step 2: 12 + 3 = 15. Step 3: 15 + 3 = 18. Answer: 15, 18
2
Worked Example
What is the missing term? 1, 2, 4, 8, ___, 32
SolutionStep 1: 2 ÷ 1 = 2, 4 ÷ 2 = 2, 8 ÷ 4 = 2. Rule = ×2 each time. Step 2: 8 × 2 = 16. Step 3: Check: 16 × 2 = 32. Answer: 16
3
Worked Example
A pattern starts at 5 and adds 7 each time. Write the first 5 terms.
SolutionTerm 1: 5. Term 2: 5 + 7 = 12. Term 3: 12 + 7 = 19. Term 4: 19 + 7 = 26. Term 5: 26 + 7 = 33. Pattern: 5, 12, 19, 26, 33

Key Points

  • A growing pattern gets larger with each term
  • Add patterns: find the difference between consecutive terms
  • Multiply patterns: find what you multiply each term by
  • Always check your rule works for at least two pairs of terms
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.A growing pattern:
Explanation: Increases by a fixed rule.
Q2.The rule of $2, 4, 6, 8$ is:
Explanation: Add $2$.
Q3.The next term of $5, 10, 15$ is:
Explanation: Add $5$.
Q4.The rule of $3, 6, 12, 24$ is:
Explanation: Double each time.
Practice more MCQs → 📝 Assignment · 35 marks