Mental Reasoning 1- Series: Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways
Mental Reasoning based on Series is one of the most common and high-scoring parts of Reasoning Ability in competitive exams like SSC, RRB, Banking, Defence, or State PSCs.
Let’s go step-by-step from the basics to advanced, covering all major types, concepts, and examples with tricks.
1. What is a Series in Mental Reasoning?
A series is a sequence of numbers, letters, or figures arranged in a specific logical order. So one has to find the pattern and predict the next/missing/wrong term.
MAIN TYPES OF SERIES QUESTIONS
There are five main types, with several subtypes:
| Category | Description | Examples |
| Number Series | Numbers follow a pattern | 2, 4, 8, 16,? |
| Alphabet Series | Letters follow a pattern | A, C, E, G,? |
| Alphanumeric Series | Mix of numbers & letters | A1, B2, C3, ? |
| Mixed Series | Includes letters, numbers & symbols | A1$, B2%, C3&, ? |
| Logical / Figurative Series | Shapes, positions, and directions follow a pattern | Square → Triangle → Pentagon →? |
2. NUMBER SERIES — Types & Tricks
Type 1: Simple Addition / Subtraction
- Pattern: Constant or increasing difference.
Example:
5, 8, 11, 14,?
➡ Difference = +3
Next term = 17
Type 2: Multiplication / Division
- Pattern: Multiply or divide by a constant.
Example:
2, 4, 8, 16,?
➡ Multiply by 2
Next term = 32
Type 3: Combination (Add + Multiply)
Example:
3, 6, 7, 14, 15, 30,?
➡ ×2, +1, ×2, +1 …
Next term = 31 × 2 = 62
Type 4: Square / Cube Pattern
Example:
1, 4, 9, 16, 25,?
➡ Squares (1², 2², 3², 4², 5²…)
Next = 6² = 36
Type 5: Prime / Fibonacci Series
Example (Prime): 2, 3, 5, 7, 11, 13,__? → ✅ 17
Example (Fibonacci): 1, 1, 2, 3, 5, 8, 13,__? → ✅ 21 ( Fibonacci is a sequence in which each element is the sum of the two elements that precede it .)
Type 6: Difference of Differences
Example:
3, 6, 11, 18, 27,___?
➡ 3, 5, 7, 9 → Difference increases by +2
Next difference = 11 → 27 + 11 = 38
Type 7: Alternating Pattern
Example:
2, 4, 3, 6, 4, 8, ___?
➡ +2, ×1.5 alternately
Next = 5
Type 8: Geometric / Exponential Growth
Example: 2, 4, 8, 16, 32 → multiply by 2 each time.
3. ALPHABET SERIES — Types & Tricks
Type 1: Continuous Sequence
Example: A, C, E, G,….?
➡ +2 letters each time
Next = I
Type 2: Reverse Alphabet Order
Example: Z, X, V, T,….?
➡ -2 each time
Next = R
Type 3: Alternate Pattern
Example: A, Z, B, Y, C, X,….?
➡ 1st series → A, B, C…
➡ 2nd series → Z, Y, X…
Next = D, W
Type 4: Skipping Pattern
Example: A, D, H, M,….?
➡ +3, +4, +5 …
Next = S
Type 5: Position Code Pattern
(A=1, B=2, …, Z=26)
Example: 3, 6, 9 correspond to C, F, I
4. ALPHANUMERIC SERIES
Here, letters and numbers are combined.
You need to find a pattern in both parts.
Example:
A1, B2, C3, D4, ?
➡ Letters +1, Numbers +1
Next = E5
Example:
A2, C4, E6, G8, ?
➡ Letters +2, Numbers +2
Next = I10
Example:
1A, 2B, 4C, 8D, ?
➡ Numbers ×2, Letters +1
Next = 16E
5. MIXED SERIES (With Symbols)
Example:
A1$, B2%, C3&, D4#, ?
➡ Letters +1, Numbers +1, Symbols fixed pattern
Next = E5@
Example:
Z9#, X8$, V7%, ?
➡ Letters -2, Numbers -1
Next = T6^
6. LOGICAL / FIGURATIVE SERIES
These are non-verbal reasoning types — appear in SSC, RRB, NDA, etc.
🔸 Type 1: Shape Change
Square → Pentagon → Hexagon → ?
Heptagon
🔸 Type 2: Rotation / Flip
Arrow pointing ↑ → → ↓ → ?
Next = ←
🔸 Type 3: Shading / Counting Parts
Patterns alternate in shading, dot positions, or line counts.
7. Special & Trick Series
| Pattern Type | Example | Trick |
| Multiplying + Adding | 2, 5, 11, 23, 47 | ×2 + 1 |
| Odd–Even Separate | 3, 6, 9, 7, 14, 21 | Odd → +3, Even → ×2 |
| Square + Add | 1, 2, 6, 15, 31, ? | +1², +2², +3², +4² → Next +5²=25 → 56 |
8. Shortcut Strategy
Observe the difference/ratio
Check alternate terms
See if it involves squares/cubes/primes
Watch for repetition or interleaving
Convert letters → positions (A=1…Z=26)
Look for increasing, decreasing, or reverse patterns
9. Common Question Types in Exams
| Question Type | Example |
| Find next term | 2, 4, 8, 16,? |
| Find the missing term | 3, 9, ?, 81 |
| Find the wrong term | 1, 4, 9, 15, 25 |
| Find pair/relation | A1 : B2 :: C3 : ? |
| Coded pattern | AZ, BY, CX,? |
10. PRACTICE EXAMPLES (With Solutions)
Q1: 1, 2, 6, 24, 120,?
→ Multiply by 1, 2, 3, 4, 5 → ✅ Next = 720
Q2: 2, 6, 12, 20, 30,?
→ Difference: +4, +6, +8, +10 → ✅ Next = 42
Q3: A, D, I, P, ?
→ +3, +5, +7 → ✅ Next = Y
Q4: B1, D4, F9, H16, ?
→ Letters +2, Numbers are squares (1, 4, 9, 16) → ✅ Next = J25
Q5: 5, 10, 20, 40, ?, 160
→ ×2 pattern → ✅ Missing = 80
11. Practice Tip
- Easy to Hard order: Number → Alphabet → Alphanumeric → Mixed → Figural
- Time-saving trick: If the difference keeps changing → write 2nd difference
- Practice 10–15 questions per type daily.