Page 1 · Introduction
Finding the rule
A sequence is a list of numbers that follows a rule. The whole skill is working out the rule from the numbers you can see, then using it to find the next one. Once you can name the rule, the answer follows easily.
The big ideaLook at how you get from one number to the next. Is it adding the same amount? Multiplying? Or a two-step rule like ‘times 2, then add 1’? Name the rule, then apply it.
💡We start with simple adding patterns and build up to multiply-and-add rules. Take each step in turn.
On the real testWhere this appearsNumber patterns appear across Mathematical Reasoning and Thinking Skills (each 25% of your mark, no calculator from 2025) — and being quick at them saves time for harder questions.
Page 2 · Adding patterns
Same step each time
The simplest sequences add (or subtract) the same amount every time. Find the gap between two numbers, check it’s the same throughout, then continue it.
Find the next number: 3, 7, 11, 15, ?
Each step adds 4 (3→7→11→15). So the next is 15 + 4 = 19.
19
Find the next number: 40, 34, 28, 22, ?
Each step subtracts 6. So 22 − 6 = 16.
16
Page 3 · Multiplying patterns
Times the same number
Some sequences multiply by the same number each time. The numbers grow quickly, which is a clue.
Find the next number: 2, 6, 18, 54, ?
Each step multiplies by 3 (2×3=6, 6×3=18…). So 54 × 3 = 162.
162
Find the next number: 1, 2, 4, 8, 16, ?
Each step multiplies by 2. So 16 × 2 = 32.
32
Page 4 · Two-step & special patterns
Trickier rules
Harder sequences use a two-step rule, or a changing gap. Two famous ones: the gaps grow, or each number is the sum of the two before it.
Find the next number: 1, 2, 4, 7, 11, ?
The gaps grow: +1, +2, +3, +4… so the next gap is +5. 11 + 5 = 16.
16
Find the next number: 1, 1, 2, 3, 5, 8, ?
Each number is the sum of the two before it (3+5=8, 5+8=13). So the next is 13.
13
Level 1 · Easy
Warm up
Simple adding and subtracting patterns. Tap to check.
1. Find the next number: 5, 10, 15, 20, ?
Adds 5 each time. 20 + 5 = 25.
2. Find the next number: 2, 4, 6, 8, ?
Adds 2 each time. 8 + 2 = 10.
3. Find the next number: 30, 27, 24, 21, ?
Subtracts 3 each time. 21 − 3 = 18.
Level 2 · Medium
Building up
Bigger steps and multiplying patterns.
1. Find the next number: 7, 14, 21, 28, ?
Adds 7 each time. 28 + 7 = 35.
2. Find the next number: 3, 9, 27, 81, ?
Multiplies by 3 each time. 81 × 3 = 243.
3. Find the next number: 100, 90, 80, 70, ?
Subtracts 10 each time. 70 − 10 = 60.
Level 3 · Hard
Getting tougher
Growing gaps and two-step rules.
1. Find the next number: 2, 5, 10, 17, 26, ?
Gaps grow: +3, +5, +7, +9, so next gap is +11. 26 + 11 = 37.
2. Find the next number: 1, 3, 6, 10, 15, ?
Gaps grow by one each time: +2,+3,+4,+5, next +6. 15 + 6 = 21.
3. Find the next number: 2, 3, 5, 8, 13, ?
Each number is the sum of the two before (5+8=13, 8+13=21). Next is 21.
Level 4 · Challenge
Challenge
Multi-step reasoning. Take your time.
1. Find the next number: 1, 4, 9, 16, 25, ?
These are square numbers: 1², 2², 3², 4², 5². Next is 6² = 36.
2. Find the next number: 2, 6, 12, 20, 30, ?
Gaps grow: +4, +6, +8, +10, so next +12. 30 + 12 = 42.
3. Find the next number: 3, 6, 12, 24, 48, ?
Each number doubles. 48 × 2 = 96.
Page 9 · Well done
You’ve finished Number Patterns & Sequences
You can now spot adding, subtracting and multiplying patterns, growing gaps, and special sequences like squares and Fibonacci. Naming the rule is the key to every one.
RememberLook at how each number turns into the next. Add? Multiply? Growing gap? Name the rule, then apply it.
🎉Great work getting through all four tiers. Try another module next — every one builds a different skill.
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