🧩 Number 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:
• Look at two consecutive terms
• Find the difference (for add) or ratio (for multiply)
• Check it works for the next pair too
• Apply the rule to find the next term

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).

An input-output table shows pairs of numbers connected by a rule — like a machine that transforms the input into the output.
The rule can be:
• Add or subtract: Input 3 → Output 8 (Rule: +5)
• Multiply or divide: Input 4 → Output 12 (Rule: ×3)
• Two-step rule: Input 2 → Output 5 (Rule: ×2+1)

How to find the rule:
• Look at the first input-output pair
• Try simple operations (+, -, ×, ÷)
• Test your rule on at least two more pairs
• If it works for all pairs, you have the rule

Once you know the rule, you can find any output for any input.