Series Completion

Series Completion requires you to find the missing term in a sequence. SSC CGL tests these main types:

1. Number Series: Arithmetic (add/subtract same number), Geometric (multiply/divide), Mixed (alternate operations), Square/Cube series, Prime number series
2. Letter Series: Alphabetical order forward/backward, skip-letter patterns, position-based patterns
3. Alpha-Numeric Series: Combination of numbers and letters following mixed rules
4. Wrong Number Series: Find the term that breaks the pattern

Step-by-step approach:

• Step 1: Check difference between consecutive terms (add/subtract pattern)
• Step 2: Check ratio of consecutive terms (multiply/divide pattern)
• Step 3: If neither, check if squares/cubes are involved
• Step 4: Check if two alternating series are mixed together

Memory Trick — Write differences between terms first. If differences are constant → arithmetic. If differences themselves form a pattern → higher-order arithmetic.

Common Number Series Formulas for SSC CGL:

1. Arithmetic Series: aₙ = a₁ + (n-1)d
   where a₁ = first term, d = common difference

2. Geometric Series: aₙ = a₁ × rⁿ⁻¹
   where r = common ratio

3. Squares Series: 1, 4, 9, 16, 25, 36… (n²)

4. Cubes Series: 1, 8, 27, 64, 125… (n³)

5. Fibonacci-type: Each term = sum of previous two

6. Difference of Differences: When 1st difference is not constant, find 2nd difference

Quick Reference — Prime numbers up to 50:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Perfect Squares to memorize: 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225
Perfect Cubes: 1,8,27,64,125,216,343,512,729,1000

Example 1 (Number): 3, 7, 13, 21, 31, ?
Differences: 7-3=4, 13-7=6, 21-13=8, 31-21=10. Differences are 4,6,8,10 — increasing by 2. Next difference = 12. So answer = 31+12 = 43.

Example 2 (Letter): B, E, H, K, ?
B(2), E(5), H(8), K(11) — each letter's position increases by 3. Next = 11+3 = 14 = N. Answer: N.

Example 3 (Mixed): 2A, 4C, 6E, 8G, ?
Numbers: 2,4,6,8 → add 2 → next is 10. Letters: A,C,E,G → skip one letter → next is I. Answer: 10I.

Example 4 (Wrong term): 4, 9, 20, 43, 90, 183
Pattern: ×2+1 → 4×2+1=9, 9×2+2=20, 20×2+3=43, 43×2+4=90, 90×2+5=185 ≠ 183. Wrong term is 183.

Quick-revision notes for Series Completion — the must-know points for SSC CGL Tier-I/II.

• Verbal/alphabet series give a sequence of letters or letter-number groups following a hidden rule; find the next term or the missing term.
• Check the step between consecutive letters — constant (+2, +3), increasing (+1,+2,+3…), or alternating steps for two interleaved series.
• Write positional numbers under the letters to convert the pattern into arithmetic you can extend easily.
• Alternate-series trick: odd-position and even-position letters often follow two separate patterns — solve them independently.
• Mixed letter-number series combine an alphabet rule with a number rule running in parallel; track both columns.
• Always verify your rule reproduces every given term before selecting the missing one.

Cover the answer, recall, then check. 6 cards on the must-know Series Completion facts for SSC CGL.

Q1. Find the next term: A, C, E, G, ?
A1. I — letters increase by +2 each (skip one letter every step).

Q2. Complete: B, D, G, K, ?
A2. P — gaps increase +2, +3, +4, +5 (B+2=D, D+3=G, G+4=K, K+5=P).

Q3. Why write positional numbers below the letters?
A3. It converts the letter pattern into simple arithmetic, making the step size obvious and easy to extend.

Q4. Series: AZ, BY, CX, ? — what next?
A4. DW — first letters go forward A,B,C,D; second letters go backward Z,Y,X,W.

Q5. How do you handle an "alternate" series like A, 2, C, 4, E, ?
A5. Split it: letters A,C,E (+2) and numbers 2,4 (+2) → next is 6.

Q6. First step when a series looks random?
A6. Look for two interleaved sub-series (alternate terms) before assuming a single complex rule.