Number sequences
Find the missing term by working out the rule that generates the sequence.
What the question asks
You are given a run of numbers with one missing, and you must work out the rule that generates them.
3, 7, 11, 15, ___
Each term is 4 more than the last, so the answer is 19.
Finding the rule: check differences first
Write the gaps between consecutive terms. If the gaps are all the same, the rule is "add n" and you are done. If the gaps themselves form a pattern, look one level deeper.
- Constant difference — 3, 7, 11, 15 (gaps of 4)
- Growing difference — 2, 3, 5, 8, 12 (gaps of 1, 2, 3, 4)
- Multiply — 3, 6, 12, 24 (double each time)
- Two interleaved sequences — 1, 10, 2, 20, 3, 30 (odd and even positions run separately)
If the differences make no sense, try ratios. If ratios make no sense, check whether alternate terms form their own sequence — interleaving is the most commonly missed pattern.
How to attack this question type
- 1
Always write the differences between terms first. Most sequences at this level resolve immediately, and it costs you three seconds.
- 2
If the differences are not constant, take the differences OF the differences. A constant second difference means the rule involves squares.
- 3
Numbers that grow very fast usually mean multiplication, not addition. Numbers that rise and fall usually mean two interleaved sequences.
- 4
Check your rule against EVERY term, not just the first two. A rule that fits the first pair and fails the third is the trap.
- 5
EduTest gives no working-out paper, so practise holding the differences in your head — writing them down is not an option on the day.
Practice · untimed
What is the next number in this sequence?
2, 3, 5, 8, 12, ___
More in Numerical Reasoning
Ratio and proportion
Share a quantity in a given ratio, or scale one quantity against another.
Rates and work
Scale a rate — workers, speed, cost per unit — up or down to a new quantity.
Age problems
Relate two ages now and at another time, then solve for one of them.
Sequences — missing number
Pairs or a small grid follow one rule; work the rule out and fill in the hidden number.
Sequences — find the rule
A run of numbers was built by one rule; choose the written rule that fits every step.
Sequences — odd one out
Every number is shown and one of them breaks the pattern the rest follow; find it.