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Professional and Subprofessional · Civil Service Exam

Number and letter series

A series question gives you four or five terms and asks for the next one. The whole task is naming the rule that produced them.

Series items are the most mechanical part of the numerical section, and the most reliably winnable: the answer is not a matter of judgement, so once you can name the rule you have the mark. Work the differences between consecutive terms first. If those are constant the rule is addition; if the differences themselves form a pattern, the rule sits one level down.

When differences lead nowhere, try ratios. Then try the possibility that two sequences are interleaved - odd positions following one rule and even positions another - which looks chaotic until you split it and then becomes obvious.

Letter series work the same way with position numbers standing in for values: A is 1, B is 2, and a constant step in the alphabet is a constant difference in disguise. Blocks of letters step together.

Worked examples

Try these, then read why.

Written for this platform and generated from the same bank the practice sets draw on. Every wrong option is explained, because knowing why a distractor was tempting is most of the learning.

What number completes the series?

15, 22, 29, 36, 43, 50, ___
  1. A43
  2. B57 (correct)
  3. C64
  4. D50

The series follows one rule throughout: each term is 7 more than the one before it. Applying that rule to the last printed term gives 57. Check a rule against every printed term before continuing a series; a rule that explains only the first pair is usually the wrong one.

  • A This moves backwards through the series instead of forwards.
  • C This continues the series one term too far.
  • D This repeats the last printed term instead of continuing the series.

What number completes the series?

3, 9, 21, 39, 63, 93, ___
  1. A135
  2. B93
  3. C129 (correct)
  4. D87

The series follows one rule throughout: the differences between terms start at 6 and grow by 6 each time. Applying that rule to the last printed term gives 129. Check a rule against every printed term before continuing a series; a rule that explains only the first pair is usually the wrong one.

  • A This continues the series one term too far.
  • B This repeats the last printed term instead of continuing the series.
  • D This moves backwards through the series instead of forwards.

What comes next in the series?

G, I, K, M, O, Q, ___
  1. AU
  2. BS (correct)
  3. CR
  4. DT

The series follows one rule throughout: each letter is 2 places after the previous one in the alphabet. Applying that rule to the last printed term gives S. Check a rule against every printed term before continuing a series; a rule that explains only the first pair is usually the wrong one.

  • A This is 2 letters away from the letter the pattern requires.
  • C This is 1 letter away from the letter the pattern requires.
  • D This is 1 letter away from the letter the pattern requires.

Practise this properly.

Three examples show you the format. Finding out whether number and letter series is actually costing you marks takes a measured set, which is what the free diagnostic is for.

Take the free diagnosticHow it works

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