Series and Analogy

Why This Chapter Matters

Series (number, letter, mixed) and Analogy together give 6-10 marks in SSC CGL and CHSL. These are the most consistent questions — same pattern repeated every year.

Part 1 — Number Series

Types of Series

Difference series: Find the pattern in differences.

2, 5, 10, 17, 26, ? → Differences: 3,5,7,9,11 (odd numbers) → next diff=11 → 26+11=37.

Ratio series: Each term = previous × fixed number.

3, 6, 12, 24, ? → ratio=2 → next=48.

Square/Cube series:

1, 4, 9, 16, ? → Perfect squares → 25.

2, 9, 28, 65, ? → (1³+1, 2³+1, 3³+1, 4³+1) → 5³+1=126.

Mixed operations:

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

Two-step patterns:

+2, +4, +2, +4... | +1,+3,+1,+3... | alternating operations.

Approach: Find difference between consecutive terms. If differences have a pattern → done. If not, check ratio. If not, check second differences (differences of differences).

Common SSC Patterns

n² series: 1,4,9,16,25,36...

n²+1: 2,5,10,17,26...

n²-1: 0,3,8,15,24...

n(n+1): 2,6,12,20,30...

Fibonacci: 1,1,2,3,5,8,13,21...

Part 2 — Letter/Alphabet Series

Positions: A=1, B=2...Z=26. Or from end: A=26, Z=1.

Pattern: Find position differences.

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

Reverse alphabet: Z=1, Y=2...A=26.

Letter pairs: AC, EG, IK, MO, ? → vowels +2 → QS.

Part 3 — Analogy

Word Analogy

Find the relationship in the first pair, apply to the second.

Doctor : Hospital :: Teacher : School (person : workplace)

Book : Library :: Money : Bank (things : where they are stored)

Hammer : Carpenter :: Stethoscope : Doctor (tool : user)

Eye : See :: Ear : Hear (organ : function)

Common relationships:

Tool-user | Part-whole | Worker-workplace | Thing-material

Animal-young | Animal-sound | Degree of intensity | Cause-effect

Opposite | Synonym | Country-capital | Country-currency

Number Analogy

16:4 :: 25:5 (perfect squares : square roots)

8:512 :: 5:125 (n:n³)

Find operation connecting pair 1, apply to pair 2.

Letter Analogy

ACE : FHJ :: KMO : ? → both skip one letter, shift +5 → PRT.

Solved Examples

Q1 (Series): 7, 12, 19, 28, 39, ?

Differences: 5,7,9,11 (adding 2 each time) → next diff=13 → 39+13=52.

Q2 (Analogy): Dog : Kennel :: Horse : ?

Dog lives in Kennel. Horse lives in Stable. Answer: Stable.

Q3 (Letter series): B, D, G, K, P, ?

Differences: 2,3,4,5,6 → P(16)+6=22=V. Answer: V.

PYQs (SSC)

SSC CGL 2023 (Series): 3, 7, 15, 31, 63, ?

Pattern: ×2+1 → 3×2+1=7, 7×2+1=15... → 63×2+1=127.

SSC CGL 2022 (Analogy): ACFJ : BDHK :: MOSX : ?

A+1=B, C+1=D, F+2=H, J+1=K. Pattern: +1,+1,+2,+1 → M+1=N, O+1=P, S+2=U, X+1=Y → NPUY.

Revision Notes

NUMBER SERIES APPROACH:
Step 1: Find differences | Step 2: If pattern → done
Step 3: If not, find ratio | Step 4: Check second differences
Step 5: Try n², n³, n(n+1) patterns

LETTER POSITIONS: A=1...Z=26 | From end: Z=1...A=26

ANALOGY RELATIONSHIPS:
Tool-User | Part-Whole | Worker-Workplace | Animal-Young
Animal-Sound | Country-Capital | Cause-Effect | Degree

COMMON OPERATIONS IN NUMBER ANALOGY:
n² | n³ | n(n+1) | 2n+1 | n+prime | n²+k