Series — SSC CGL Reasoning

Every series question hides a generator — the rule that makes each term from the last (or from its position). SSC draws from a small menu of generators and disguises them with size. The method is always identical: write the gaps, then the gaps of the gaps. Two rows of differences expose almost every SSC series ever set.

1. What SSC actually asks

Tier 1: 3–4 questions · Tier 2: 4–5 questions, in three skins:

1. Missing-term number series — "7, 12, 22, 37, 57, ?"
2. Wrong-term number series — "3, 7, 16, 35, 70, 153 — which term is wrong?"
3. Letter / alphanumeric series — "AZ, BY, CX, ?" or "Z, X, U, Q, ?"
4. Figural series — the visual version; transforms live in the Non-Verbal chapter.

2. The generator menu (test in this order)

The universal opener: write first differences. If they're not obviously patterned, write second differences. If those are constant → quadratic generator (n² family). If differences multiply, switch to ratios.

Big jumps (terms triple or more) → test ratios first, not differences.

3. Wrong-term questions — the reverse game

Find the generator that fits most terms; the term that breaks it is the answer.

Example: "3, 7, 16, 35, 70, 153 — find the wrong term."

Plain ×2+1 fails at the third term (7→15, not 16), so try a growing additive: ×2 + n:

$3\times 2+1=77\times 2+2=1616\times 2+3=3535\times 2+4=7474\times 2+5=153$

The rule reproduces every given term except one — the paper says 70 where the rule says 74, and the rule still lands exactly on the final term 153 when continued from 74. So 70 is the wrong term.

Lesson: in wrong-term questions, confirm your rule on the terms after the suspect — the final term is the referee. A rule that only works before the suspect is a coincidence.

4. Letter series — three standard machines

1. Single-letter chains with growing skips: Z, X, U, Q, ? → gaps −2, −3, −4 → next −5 → L.
2. Letter-pair machines: AZ, BY, CX → first letters +1, second letters −1 → DW. (Mirror pairs again — positions sum to 27.)
3. Block series: A, C, F, J, O → +2, +3, +4, +5 → U.

Alphanumeric mixes ("K2, M6, O12, Q20, ?") run two independent machines: letters +2 (K, M, O, Q → S); numbers are $n(n+1)$: 2, 6, 12, 20 → 30. Answer S30. Always split the tracks.

Cyclic counting: positions wrap mod 26 — after Z comes A. For "repeated word" questions ("which letter is 4th to the left of the 9th letter from the right of the alphabet") — anchor with EJOTY, draw the 26-slot line once.

5. Solved PYQ-style examples

Q1. 11, 13, 17, 25, 41, ? Solution. Gaps: 2, 4, 8, 16 → next gap 32 → 73. (Gaps double — a ratio pattern inside the differences.)

Q2. 6, 9, 18, 45, 126, ? Solution. Ratios: 1.5, 2, 2.5, 2.8…? Test differences: 3, 9, 27, 81 → powers of 3 → next difference 243 → 369.

Q3. 5, 6, 14, 45, 184, ? Solution. ×1+1, ×2+2, ×3+3, ×4+4 → next ×5+5 = 184×5+5 = 925.

Q4. Find the wrong term: 2, 6, 12, 20, 31, 42. Solution. Expected $n(n+1)$: 2, 6, 12, 20, 30, 42 → 31 is wrong (should be 30).

Q5. BD, GI, LN, QS, ? Solution. Within pairs: +2 (B→D). Between pairs: +5 (B→G→L→Q→V) → VX.

Q6 (Tier 2). 3, 5, 9, 17, 33, ? Solution. Gaps 2, 4, 8, 16 → +32 → 65. Equivalent generator: ×2 − 1. Both give 65 — when two rules agree, confidence is free.

6. Exam protocol

1. Write the gaps under the series; then gaps-of-gaps if needed. Paper, not head.
2. Terms growing ≥3× per step → test ratios/mixed (×k ± m) first.
3. Interleaved suspicion (zig-zag sizes) → split into odd/even position tracks immediately.
4. Wrong-term: derive the rule from clean stretches, confirm on the terms after the suspect.
5. Letter series: convert to positions, run the same difference machinery; split alphanumeric tracks.
6. 30-second cap in Tier 1; a series that resists two difference rows is a skip candidate.