Number & Letter Series

Snapshot

• Number & Letter Series shows a sequence with one term missing (or wrong) and asks for it. The whole skill is spotting the pattern — usually in the differences between terms, or in a multiplication, or in squares/cubes/primes.
• Letter series run on alphabet position (A = 1 … Z = 26), so knowing positions instantly is half the battle.
• This guide covers every common pattern type, the difference method, letter and alternating series, and the "wrong term" variant — with worked examples.
• Exam reality: +5 / −1. Find the rule, then apply it; don't force-fit.

Part 1 — Number series: find the rule

The reliable first move is to write the differences between consecutive terms. If the differences are constant it's arithmetic; if they grow steadily, take the second differences. Other common engines:

• Multiplicative: each term × a constant (3, 6, 12, 24 — ×2).
• Squares / cubes: 1, 4, 9, 16, 25 (n²) or 1, 8, 27, 64 (n³); also n²±1, n²+n.
• Primes: 2, 3, 5, 7, 11, 13.
• Mixed / two-step: ×2 then +1 alternately, or "+2, ×2, +2, ×2".
• Alternating: two interleaved series — look at the odd and even positions separately.

Part 2 — Letter & alpha-numeric series

Convert letters to positions and the pattern usually appears at once. Series may skip a fixed gap (A, C, E, G — +2), reverse (Z, X, V — −2), or pair a letter with a number. For "opposite letter" steps, use the mirror rule (A↔Z, B↔Y; the two positions add to 27).

Part 3 — The "wrong term" variant

Some questions give a series with one term that breaks the rule and ask you to spot it. Establish the pattern from the first few correct terms, then find the term that does not fit.

Part 4 — Speed techniques

1. Write the differences first — it cracks the majority of number series.
2. If differences grow, check the second differences (often constant, e.g. squares).
3. Test ÷ and × early when the numbers jump fast.
4. Split alternating series into odd- and even-placed terms.
5. Keep the EJOTY anchors (A1, E5, J10, O15, T20, Y25) to read letter positions instantly.

Part 5 — Worked examples

1. 3, 7, 13, 21, 31, ? Differences 4, 6, 8, 10 (rise by 2) → next +12 → 43.

2. 5, 11, 23, 47, ? Each ×2 + 1 → 47 × 2 + 1 = 95.

3. 1, 4, 9, 16, 25, ? Squares of 1–5 → 6² = 36.

4. 2, 6, 12, 20, 30, ? n² + n (1·2, 2·3, 3·4 …) → 6·7 = wait, pattern is n(n+1): 30 = 5·6, next 6·7 = 42.

5. A, C, F, J, ? Gaps +2, +3, +4 → next +5 from J(10) → O(15) = O.

6. 3, 9, 27, 81, ? × 3 each → 243.

7. Z, W, T, Q, ? −3 each (26, 23, 20, 17) → 14 = N.

8. Find the wrong term: 2, 5, 10, 17, 27, 37. Pattern +3, +5, +7, +9 gives 2,5,10,17,26,37 → 27 is wrong (should be 26).

Part 6 — Common traps

• Forcing one rule when it's alternating — split the series.
• Missing second-level differences (squares hide here).
• Letter gaps — count positions, don't eyeball the alphabet.
• Off-by-one on positions — A is 1, not 0.

Part 7 — How to use this page

Memorise the EJOTY anchors and the difference method, re-solve the eight examples writing the differences, then attempt the practice set and the timed test.

One-line revision: write the differences first, check second differences and ÷/× for fast jumps, split alternating series, and read letters by position using the EJOTY anchors.