Number Series
Number Series is an 11+ verbal reasoning question type where pupils are given a sequence of numbers with the last term missing and must work out the mathematical rule linking consecutive terms, such as a constant difference, a constant multiplier, or a difference that itself changes. It appears throughout GL Assessment and CEM-style papers and tests pattern-spotting speed without a calculator.
Method
- Find the difference, or the ratio, between each pair of consecutive numbers and write these down.
- Check whether the difference stays the same, changes by a constant amount each time, or whether each term is multiplied or divided by the same number.
- If the simple checks do not work, try adding the two previous terms together, or check for two sequences woven together as alternating terms.
- Once you have found the rule, apply it once more to the last given term to work out the missing number.
- Check your answer matches one of the five options exactly before moving on.
- If your rule does not match any option, re-check your differences for an arithmetic slip before trying a more complex rule.
Worked example
3, 7, 11, 15, 19, ? A) 21 B) 22 C) 23 D) 24 E) 25.
- Find the difference between consecutive terms: 7-3=4, 11-7=4, 15-11=4, 19-15=4.
- The difference is constant at 4, so this is a simple arithmetic sequence: add 4 each time.
- Apply the rule to the last term: 19+4=23.
- Final answer: C) 23.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Find the next number in this series and identify the rule you used: 9, 18, 27, 36, 45, ? A) 48 B) 50 C) 54 D) 55 E) 63.
Find the next number in this series and show your working: 4, 5, 7, 10, 14, ? A) 17 B) 18 C) 19 D) 20 E) 21.
Find the next number in this series: 500, 100, 20, 4, ? A) 0.4 B) 0.5 C) 0.8 D) 1 E) 2.
Free printable worksheet
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