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Verbal Reasoning · Guide 6 of 8

Number and letter series

A series is a list that follows a rule. Find the rule by looking at the gaps, and the next number or letter pair follows.

  • Ages 9 to 11
  • 11+ Verbal Reasoning
  • Worked examples

What is it?

In a number series you find the next number (or a missing number) in a list such as 3, 7, 11, 15, ?. In a letter series you find the next pair of letters, such as AB, CD, EF, ?.

The rule can be adding or taking away the same amount, a gap that grows, multiplying, square numbers, or two separate series taking turns.

A typical question

2, 3, 5, 8, 12, ?

How to spot it

  • A list of numbers or letter pairs separated by commas, with a gap or question mark.
  • Letter series questions often say 'Use the alphabet to help you'.
  • The missing item might be at the end or in the middle.

Step-by-step method

  1. Step 1: Write the difference between each pair of neighbours above the gaps (+4, +4, +4…).
  2. Step 2: If the differences are the same, carry on. If they change, look at the differences themselves (+1, +2, +3…).
  3. Step 3: No pattern? Try ×2, ÷2 or square numbers (1, 4, 9, 16…).
  4. Step 4: Still stuck? Look at every other number: there may be two series taking turns.
  5. Step 5: For letters, turn them into alphabet positions and do the same. Treat each letter in a pair as its own series.
  6. Step 6: Check your rule works for every step, not just the last one.

Worked examples

Example 1: the same gap

Question: 3, 7, 11, 15, ?
  1. Step 1: Gaps: +4, +4, +4.
  2. Step 2: 15 + 4 = 19.

Answer: 19

Example 2: a growing gap

Question: 2, 3, 5, 8, 12, ?
  1. Step 1: Gaps: +1, +2, +3, +4. Each gap is one more than the last.
  2. Step 2: The next gap is +5: 12 + 5 = 17.

Answer: 17

Example 3: two series taking turns

Question: 4, 20, 6, 18, 8, 16, ?
  1. Step 1: The gaps jump about (+16, −14, +12…), so look at every other number.
  2. Step 2: 1st, 3rd, 5th numbers: 4, 6, 8 (going up by 2). 2nd, 4th, 6th: 20, 18, 16 (going down by 2).
  3. Step 3: The missing number is 7th, so it belongs to the first series: 8 + 2 = 10.

Answer: 10

Example 4: a letter series

Question: BD, EG, HJ, ?
  1. Step 1: First letters: B, E, H. Each moves forward 3 (B → E → H), so next is K.
  2. Step 2: Second letters: D, G, J. Each moves forward 3 too, so next is M.

Answer: KM

Common traps

  • Looking at only the last two numbers

    Check the rule from the very start. 2, 4, 8 could be +2, +4 or ×2: the next number tells you which.

  • Missing a second series

    If the numbers go up and down, split them into odd and even positions.

  • Off the end of the alphabet

    After Z comes A again: X moved forward 4 is B.

  • Counting letters instead of jumps

    From B to E is 3 jumps (C, D, E), not 4.

Top tips

  • Know your square numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) and times tables up to 12 × 12.
  • Write the alphabet with numbers before you start letter questions.
  • Backwards series (Z, Y, X…) are common: count back just as carefully.

Practice questions

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6 practice questions on this topic, from easy to 11+ level. Reading the guide is free for everyone; practice is for members, and signing up is free.

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