Number Sequence Patterns Practice Test Worksheets
Number sequence questions ask you to find the next term in a pattern. The strongest approach is to test several pattern types: differences, alternating rules, interleaved sequences, and terms made from earlier terms.
For children who can spot simple patterns, but lose marks when the rule changes, alternates, or works backwards.
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What Do Number Sequences Questions Look Like?
Number sequence questions ask you to identify the underlying pattern in a string of numbers to find the missing terms. Patterns can involve constant differences, changing steps, or two alternating sequences. Here is a worked example.
Subtract 3 More Each Time
Question: Find the next number: 41, 37, 30, 20, 7, ___
Worked Method
Step 1: Check the differences: 41 to 37 is -4, then -7, then -10, then -13.
Step 2: The amount subtracted is increasing by 3 each time.
Step 3: Next, subtract 16: 7 - 16 = -9.
Tip: Differences can be negative, and the next answer can be below zero.
Rules to Help You Solve Number Sequences Questions
To solve number sequences like the example above, find the difference between consecutive terms first. Follow these core rules:
➕ Rule 1: Check differences first
Look at how much is added or subtracted between neighbouring terms.
Example: 41, 37, 30, 20, 7 subtracts 4, 7, 10, 13.
🔀 Rule 2: Split odd and even positions
If one rule does not fit, check the 1st, 3rd, 5th terms separately from the 2nd, 4th, 6th terms. Odd and even refer to the positions, not the numbers in them.
Example: In the sequence above, the odd positions are 5, 20, 80, 320 (×4). The even positions are 8, 10, 12, 14 (+2).
🧱 Rule 3: Try previous terms
Some sequences make the next term from the two terms before it.
Example: 11, 16, 27, 43, 70 continues with 43 + 70.
✅ Rule 4: Test the whole pattern
A rule must explain all the visible terms, not just the last two.
Example: Multiplying only the last number may ignore the even-position pattern.
Two More Worked Examples
Here are two more examples showing how to split woven sequences and avoid forcing a single gap rule.
Split Two Woven Sequences
Question: Find the next number: 5, 8, 20, 10, 80, 12, 320, ___
Worked Method
Step 1: Look at odd positions: 5, 20, 80, 320. Each term is multiplied by 4.
Step 2: Look at even positions: 8, 10, 12. Each term adds 2.
Step 3: The blank is in an even position, so 12 + 2 = 14.
Tip: If the pattern jumps between small and large changes, try odd and even positions separately.
Do Not Force a Single Gap Rule
Question: Find the next number: 11, 16, 27, 43, 70, ___
Worked Method
Step 1: The gaps are 5, 11, 16, 27. They are not constant. Try adding the previous two terms.
Step 2: Try using previous terms: 11 + 16 = 27, then 16 + 27 = 43.
Step 3: The pattern continues: 27 + 43 = 70, so the next term is 43 + 70 = 113.
The trap: Do not assume the same amount is added each time. Check the rule against every term.
