Number & Letter Series
Key Concepts & Formulas
Provide 5-7 essential concepts for Number & Letter Series:
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Arithmetic Progression (AP) | Series where difference between consecutive terms is constant (e.g., 3, 7, 11, 15… with common difference +4) |
| 2 | Geometric Progression (GP) | Series where ratio between consecutive terms is constant (e.g., 2, 6, 18, 54… with common ratio ×3) |
| 3 | Prime Number Series | Series based on prime numbers (2, 3, 5, 7, 11, 13…) |
| 4 | Letter Position Value | A=1, B=2, C=3… Z=26; convert letters to numbers to find patterns |
| 5 | Alternate Series | Two different patterns running alternately (e.g., +3, ×2, +3, ×2…) |
| 6 | Perfect Squares/Cubes | Series based on n² or n³ (e.g., 1, 4, 9, 16… or 1, 8, 27, 64…) |
| 7 | Fibonacci Series | Each term is sum of two preceding terms (e.g., 1, 1, 2, 3, 5, 8…) |
10 Practice MCQs
Q1. What is the next number in the series: 5, 10, 15, 20, ? A) 22 B) 25 C) 30 D) 35
Answer: B) 25
Solution: The series follows AP with common difference = 5 20 + 5 = 25
Shortcut: Count by 5s
Concept: Number & Letter Series - Arithmetic Progression
Q2. Find the missing letter in the series: A, C, E, ?, I A) F B) G C) H D) J
Answer: B) G
Solution: A(1), C(3), E(5), ?(7), I(9) Pattern: Odd numbers only Missing letter = 7th letter = G
Shortcut: Skip one letter each time
Concept: Letter Position Value - Odd number pattern
Q3. Which number is wrong in the series: 2, 4, 8, 16, 36, 64? A) 4 B) 8 C) 16 D) 36
Answer: D) 36
Solution: Pattern: 2¹, 2², 2³, 2⁴, 2⁵, 2⁶ Should be: 2, 4, 8, 16, 32, 64 36 is wrong (should be 32)
Shortcut: Powers of 2
Concept: Number & Letter Series - Geometric Progression
Q4. Complete the series: 3, 8, 18, 38, ? A) 58 B) 68 C) 78 D) 88
Answer: C) 78
Solution: Pattern: ×2+2, ×2+2, ×2+2… 3×2+2 = 8 8×2+2 = 18 18×2+2 = 38 38×2+2 = 78
Shortcut: Double and add 2
Concept: Number & Letter Series - Mixed operation pattern
Q5. Find the next term: B2, D4, F8, H16, ? A) J32 B) K24 C) L32 D) M16
Answer: A) J32
Solution: Letters: B(2), D(4), F(6), H(8), J(10) - even numbers Numbers: 2, 4, 8, 16, 32 - ×2 pattern Next term: J32
Shortcut: Letter position ×2 for number
Concept: Number & Letter Series - Combined letter-number pattern
Q6. A train passes stations in pattern: 121, 144, 169, ?, 225. What’s the next station number? A) 184 B) 196 C) 200 D) 216
Answer: B) 196
Solution: Pattern: 11², 12², 13², ?, 15² Missing: 14² = 196
Shortcut: Squares of consecutive numbers
Concept: Number & Letter Series - Perfect Squares
Q7. Complete: 1, 2, 6, 15, 31, ? A) 46 B) 52 C) 56 D) 64
Answer: C) 56
Solution: Pattern: +1², +2², +3², +4², +5² 1 + 1² = 2 2 + 2² = 6 6 + 3² = 15 15 + 4² = 31 31 + 5² = 56
Shortcut: Add consecutive squares
Concept: Number & Letter Series - Square addition pattern
Q8. Find wrong term: 2, 6, 12, 27, 58, 121 A) 6 B) 12 C) 27 D) 58
Answer: B) 12
Solution: Pattern: ×2+2, ×2+4, ×2+6, ×2+8, ×2+10 2×2+2 = 6 6×2+4 = 16 (not 12) 16×2+6 = 38 38×2+8 = 84 84×2+10 = 178
Shortcut: Check ×2+even number pattern
Concept: Number & Letter Series - Complex alternating operations
Q9. What comes next: 4, 6, 9, 13½, ? A) 18¼ B) 20¼ C) 22½ D) 24¾
Answer: B) 20¼
Solution: Pattern: ×1.5, ×1.5, ×1.5, ×1.5 4 × 1.5 = 6 6 × 1.5 = 9 9 × 1.5 = 13.5 13.5 × 1.5 = 20.25 = 20¼
Shortcut: Multiply by 3/2 each time
Concept: Number & Letter Series - Fractional geometric progression
Q10. Complete the complex series: 1, 4, 27, 16, 125, 36, ? A) 216 B) 343 C) 49 D) 81
Answer: B) 343
Solution: Two alternating series: Odd positions: 1³, 3³, 5³, 7³ = 1, 27, 125, 343 Even positions: 2², 4², 6² = 4, 16, 36 Next term is 7th position (odd): 7³ = 343
Shortcut: Odd positions - cubes of odd numbers
Concept: Number & Letter Series - Alternate series with powers
5 Previous Year Questions
PYQ 1. Find the missing number: 3, 8, 15, 24, ?, 48 [RRB NTPC 2021 CBT-1]
Answer: C) 35
Solution: Pattern: +5, +7, +9, +11, +13 3 + 5 = 8 8 + 7 = 15 15 + 9 = 24 24 + 11 = 35 35 + 13 = 48
Exam Tip: Look for consecutive odd number differences in railway exam series
PYQ 2. Which letter comes next: B, E, H, K, ? [RRB Group D 2022]
Answer: A) N
Solution: Positions: B(2), E(5), H(8), K(11), ? Pattern: +3 each time 11 + 3 = 14 → N
Exam Tip: Letter series often use simple arithmetic progression
PYQ 3. Find wrong term: 5, 21, 42, 67, 97, 131 [RRB ALP 2018]
Answer: B) 42
Solution: Pattern: +16, +20, +24, +28, +32 5 + 16 = 21 21 + 20 = 41 (not 42) 41 + 24 = 65 65 + 28 = 93 93 + 32 = 125
Exam Tip: Railway exams love difference patterns with constant increase
PYQ 4. Complete: 2, 3, 5, 9, 17, ? [RRB JE 2019]
Answer: C) 33
Solution: Pattern: ×2-1, ×2-1, ×2-1, ×2-1 2×2-1 = 3 3×2-1 = 5 5×2-1 = 9 9×2-1 = 17 17×2-1 = 33
Exam Tip: ×2±n is very common in RRB technical exams
PYQ 5. Find next pair: A1, C3, F6, J10, ? [RPF SI 2019]
Answer: A) O15
Solution: Letters: A(1), C(3), F(6), J(10), ? Pattern: +2, +3, +4, +5 10 + 5 = 15 → O Numbers: 1, 3, 6, 10, ? Pattern: +2, +3, +4, +5 10 + 5 = 15
Exam Tip: Combined letter-number series are frequent in RPF exams
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Perfect Squares | Remember squares up to 25 | 1,4,9,16,25,36,49,64,81,100 |
| Prime Numbers | First 15 primes by heart | 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 |
| Letter Series | Use alphabet positions | A=1,B=2…Z=26; write above letters |
| ×2 Patterns | Check if doubling works | 3,6,12,24,48… (all ÷3 = powers of 2) |
| Difference Method | Take differences twice | 1,4,10,19,31: Differences=3,6,9,12 (AP) |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Ignoring alternate patterns | Focus only on single pattern | Check odd-even positions separately |
| Not checking from both ends | Only check forward pattern | Verify reverse pattern too |
| Forgetting letter positions | Don’t memorize A=1 to Z=26 | Write alphabet with numbers for quick reference |
| Missing fractional patterns | Expect only whole numbers | Consider ÷2, ×1.5, ×0.5 patterns |
| Overlooking multiple operations | Assume single operation | Check × then +, or + then × combinations |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| 7th prime number | 17 |
| Position of letter ‘P’ | 16 |
| Formula for nth term of AP | a + (n-1)d |
| Next term: 1,1,2,3,5,8 | 13 (Fibonacci) |
| 15² | 225 |
| Wrong term: 2,3,5,8,12,17 | 12 (should be 13) |
| Letter series: D,G,J,M,? | P (+3 pattern) |
| Next cube after 64 | 125 (5³) |
| Pattern: ×3+1, gives 2,7,22,67,? | 202 (67×3+1) |
| Sum of positions: A+E+I | 1+5+9 = 15 |
Topic Connections
How Number & Letter Series connects to other RRB exam topics:
- Direct Link: Coding-Decoding (both use alphabet positions and patterns)
- Combined Questions: Blood Relations + Letter Series (coding family relations)
- Foundation For: Advanced puzzles and seating arrangement with coded conditions
- Mathematical Base: Number series concepts apply to Data Interpretation calculations
- Time Management: Mastering series saves 30-45 seconds per question in reasoning section
BETA
