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Guide

Number series: a fixed order for finding the rule

A number series shows a run of numbers and asks for the next one. The gap is built on a simple rule; the difficulty is that the rule can hide in the differences, the ratios or the alternation. Here is the order that finds it.

What to expect

Six to eight numbers, a blank, and a rule that links them. The numbers are rarely large and the arithmetic is rarely hard; the test is whether you can name the rule fast, not whether you can compute. Guessing from the numbers alone wastes the most time.

The rules behind the series

Almost every series is one of a few shapes: a steady add or subtract, a rising or falling gap, a multiply or divide, an alternation between two runs, or a rule that plays on the digits. Name the shape and the blank is arithmetic.

Tip

Look at the gaps first, not the numbers. A series that climbs by 2, 4, 6, 8 is a gap rule, and you never had to touch the values themselves.

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A fixed order

  • Write the gaps between neighbours before anything else.
  • If the gaps are flat, it is an add or subtract rule; if they climb, they are the rule.
  • If gaps fail, test ratios, then check for two alternating runs.
  • Confirm the rule on the whole series, not just the last pair, before you answer.

How to practice

Take one series at a time and write the rule as a sentence before choosing. Ten series solved with the rule named beat a hundred rushed. Speed is a side effect of naming, not of staring.

Portrait of Adrian, who takes tests at SmashMyTest
Written by
Adrian, Specialist

MSc Psychology, 7 years of test taking.

Last updated: Oct 27, 2026

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