Number and letter series for SSC CGL

A series question gives you a sequence built on a hidden rule and asks for the next term, a missing term or the one wrong term. Candidates who find series hard are usually not short of cleverness. They are short of order: they try random ideas, and if nothing clicks in twenty seconds they panic.

The fix is a fixed checking order. Run the same five or six tests every time, in the same sequence, and most series open up in well under a minute.

Where series appear in SSC CGL

Number series, letter series and alphanumeric series appear in the reasoning sections of both Tier 1 and Tier 2. They come in three forms:

• Next term: find the term that continues the series.
• Missing term: a blank sits in the middle, and you need the terms on both sides to confirm the rule.
• Wrong term: every term follows the rule except one.

Letter-repetition blanks ("a _ b b _ a…") also appear under this heading. The number of series questions varies by shift, so treat them as a steady, regular type rather than a fixed count.

The checking order

1. First differences. Subtract each term from the next. Constant, rising steadily, or a pattern of their own?
2. Second differences. If the first differences rise unevenly, take their differences.
3. Ratios. Does each term roughly double or treble? Test × k, then × k ± c.
4. Squares and cubes. Compare terms with n², n³, n² ± 1, n³ ± 1. Know squares to 30 and cubes to 15 by heart.
5. Primes. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31…
6. Two series interleaved. If nothing fits, split odd and even positions.

For letters, convert to positions first (A = 1 to Z = 26) and run the same tests on the numbers.

Six worked examples

1. 2, 5, 11, 20, 32, ?
Options: (a) 44 (b) 45 (c) 47 (d) 50

First differences: 3, 6, 9, 12. They rise by 3 each time, so the next difference is 15. 32 + 15 = 47, option (c). A candidate who sees only "differences go up" and guesses +14 lands on 46, which is why checking the step matters.

2. 2, 3, 8, 27, 112, ?
Options: (a) 560 (b) 565 (c) 570 (d) 675

Differences are 1, 5, 19, 85, with no clean pattern. The terms grow fast, so test ratios. 3 ≈ 2 × 1, 8 ≈ 3 × 2, 27 ≈ 8 × 3, 112 ≈ 27 × 4. The exact rule: 2 × 1 + 1 = 3, 3 × 2 + 2 = 8, 8 × 3 + 3 = 27, 27 × 4 + 4 = 112. Next: 112 × 5 + 5 = 565, option (b).

3. 4, 10, 8, 20, 16, 40, ?
Options: (a) 32 (b) 60 (c) 64 (d) 80

Differences swing up and down: +6, −2, +12, −4, +24. That swing is the signal to split the positions. Odd positions: 4, 8, 16. Even positions: 10, 20, 40. Each doubles. The seventh term belongs to the odd series: 16 × 2 = 32, option (a). The 80 in the options is the next even-position term, set as a trap.

4. Find the wrong term: 2, 5, 10, 17, 26, 38, 50

Compare with squares: 1, 4, 9, 16, 25, 36, 49. Each term is n² + 1, which gives 2, 5, 10, 17, 26, 37, 50. So 38 is wrong. Check the rival reading: differences 3, 5, 7, 9, 12, 12 break the odd-number step at exactly the same place, so both readings point to 38.

5. Z, X, U, Q, ?
Options: (a) K (b) L (c) M (d) N

Positions: 26, 24, 21, 17. Differences: −2, −3, −4, so the next is −5. 17 − 5 = 12 = L, option (b).

6. ABD, DEG, GHJ, ?
Options: (a) JKL (b) JKM (c) KLN (d) JLM

Positions: ABD = 1, 2, 4. DEG = 4, 5, 7. GHJ = 7, 8, 10. Inside each group the steps are +1, +2. Each group starts where the last one ended (A→D→G, all +3). The next group starts at J (10): 10, 11, 13 = JKM, option (b).

Letter-repetition series

These show a string with blanks, such as:

a _ b b _ a _ b a a _ b

Options: (a) aabb (b) abab (c) abba (d) baab

Try each option in the blanks and look for a repeating block. Option (a) fills them as a, a, b, b, giving a a b b | a a b b | a a b b, which repeats the block "aabb" three times. Option (b) gives a a b b b a a b a a b b, which has no regular block. Answer: (a) aabb. Split the full string into equal blocks of 3, 4 or 5 letters until one repeats.

Alphanumeric series

Here letters and numbers move together, often linked. In A1, C3, E5, G7, each number is the position of its letter, and letters skip one. Next: I9. Always check whether the number is tied to the letter's position before hunting for a separate number rule.

Common mistakes

Practice

1. 6, 11, 21, 36, 56, ?
   • (a) 76 (b) 81 (c) 86 (d) 91
2. 4, 9, 25, 49, 121, ?
   • (a) 144 (b) 169 (c) 196 (d) 225
3. 5, 11, 23, 47, 95, ?
   • (a) 189 (b) 190 (c) 191 (d) 193
4. Find the wrong term: 1, 8, 27, 64, 124, 216
5. C, F, J, O, ?
   • (a) T (b) U (c) V (d) W
6. 7, 12, 14, 24, 21, 48, ?
   • (a) 28 (b) 35 (c) 42 (d) 96
7. AZ, CX, EV, ?
   • (a) GT (b) GU (c) HT (d) FU
8. B2, D8, F18, H32, ?
   • (a) J50 (b) I50 (c) J48 (d) K50

Answers

1. (b) 81. Differences are 5, 10, 15, 20, so the next is 25: 56 + 25 = 81.
2. (b) 169. These are squares of consecutive primes: 2², 3², 5², 7², 11². Next is 13². 144 is 12², but 12 isn't prime.
3. (c) 191. Each term is × 2 + 1: 95 × 2 + 1 = 191.
4. 124. The terms are cubes 1³ to 6³; 5³ = 125.
5. (b) U. Positions 3, 6, 10, 15 rise by 3, 4, 5, so the next step is 6: 15 + 6 = 21 = U.
6. (a) 28. Odd positions: 7, 14, 21, 28 (+7). Even positions: 12, 24, 48 (× 2). The seventh term is odd-position. 96 would be the eighth.
7. (a) GT. First letters go A, C, E, G (+2). Each second letter is the opposite of the first (positions add to 27): G (7) pairs with T (20).
8. (a) J50. Letters skip one: B, D, F, H, J. Each number is half the square of the letter's position: 2²/2 = 2, 4²/2 = 8, 6²/2 = 18, 8²/2 = 32, 10²/2 = 50.

What to do next

1. Learn squares to 30, cubes to 15 and primes to 100; the squares, cubes and roots guide has the tables.
2. For a week, solve 15 series a day, writing the checking-order step at which each one opened.
3. Mix in letter series every day; they get rusty faster than number series.
4. Then take the same position habits into coding and decoding and analogy and classification.