Number Patterns • Topic 2 of 3

Shrinking Patterns

In a shrinking pattern, each term is smaller than the one before it. The sequence is going down.

Subtract patterns: 40, 35, 30, 25 — Rule: -5 each time
Divide patterns: 64, 32, 16, 8 — Rule: ÷2 each time

Some patterns have a changing difference — this makes them trickier.

Example: 55, 50, 44, 37, 29 — differences are -5, -6, -7, -8 — so the next difference is -9, making the next term 29 - 9 = 20.

Always check if the difference is constant (same) or changing (increasing or decreasing).

Solved Examples

Worked Example

Find the next term: 100, 90, 80, 70, ___

SolutionStep 1: 100 - 90 = 10, 90 - 80 = 10, 80 - 70 = 10. Rule = -10 each time. Step 2: 70 - 10 = 60. Answer: 60

Worked Example

Find the next term: 81, 27, 9, 3, ___

SolutionStep 1: 81 ÷ 27 = 3, 27 ÷ 9 = 3, 9 ÷ 3 = 3. Rule = ÷3 each time. Step 2: 3 ÷ 3 = 1. Answer: 1

Worked Example

Find the next term: 55, 50, 44, 37, 29, ___

SolutionStep 1: differences are 55-50=5, 50-44=6, 44-37=7, 37-29=8. The differences increase by 1 each time. Step 2: next difference = 9. Step 3: 29 - 9 = 20. Answer: 20

Key Points

A shrinking pattern gets smaller with each term
Subtract patterns: find the constant difference being subtracted
Divide patterns: find what you divide each term by
Some patterns have a changing difference — check if the gap increases or decreases

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.A shrinking pattern:

Explanation: Decreases by a fixed rule.

Q2.The rule of $20, 15, 10, 5$ is:

Explanation: Subtract $5$.

Q3.The next term of $30, 25, 20$ is:

Explanation: Subtract $5$.

Q4.The rule of $80, 40, 20, 10$ is:

Explanation: Halve each time.

Practice more MCQs → 📝 Assignment · 35 marks