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Number series, letter series and coding-decoding

A step-by-step way to find the rule in number and letter series and in letter-shift codes.

EWritten by the HomebaseWorks editorial team · reviewed 26 Oct 2026

Series and coding questions look different but use the same skill: find the rule, test it on every term, then apply it once more. Most screenings use a small set of rules, so checking them in a fixed order saves time.

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Number series: the order to check

  1. Differences. Subtract each term from the next. If the differences are constant or follow their own simple pattern, you have the rule. For 2, 6, 12, 20, 30 the differences are 4, 6, 8, 10, so the next is 30 + 12 = 42.
  2. Ratios. If the numbers grow fast, divide. 3, 9, 27, 81 multiplies by 3 each time.
  3. Squares and cubes. Look for 1, 4, 9, 16 or 1, 8, 27, 64, sometimes with 1 added or subtracted.
  4. Two series mixed. If nothing fits, look at alternate terms separately.

Always check the rule on every term, not just the first two. A rule that fits only the start is usually a trap.

Letter series

Convert letters to their positions. Knowing a few positions by heart makes this much faster:

A=1  E=5  J=10  O=15  T=20  Y=25
A C F J O ?
1 3 6 10 15 -> gaps 2,3,4,5 -> next gap 6 -> 21 = U

Coding-decoding

For letter codes, write the word and its code one above the other and find the shift for each letter.

M A N G O
O C P I Q   (each +2)

Common rules are a fixed shift forward or back, reversing the word, or the opposite letter, where A pairs with Z and B with Y. For opposite letters, the positions add up to 27.

Watch for wrap-around: with a shift of +2, Y becomes A and Z becomes B.

Odd one out and analogies

For odd-one-out questions, test simple properties: even or odd, prime, perfect square, multiple of a number. For analogies, put the relationship into a short sentence first, such as "a doctor works in a hospital", then test each option with the same sentence.

Habit to build: write the differences or the letter positions under the series every time, even when you think you can see the rule. It takes a few seconds and stops most careless errors.

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