Mental Reasoning 4- Number Series: Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways

Mental Reasoning 4- Number Series: Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways

Let’s now cover the entire topic of “Number Series” as it appears in competitive exams, from basic to advanced, including all likely and probable types so you can tackle 100% of exam questions confidently.

What is a Number Series? (संख्या श्रेणी क्या होती है?)

A Number Series is a sequence of numbers arranged in a specific logical pattern.
The logic can involve addition, subtraction, multiplication, division, squares, cubes, or a combination of these.

Your task in the exam is usually to:

• Find the next term, or
• Find the missing term, or
• Find the wrong term.

Example:
2, 4, 6, 8, ? → Pattern: +2 → Next term = 10

In Hindi:
संख्या श्रेणी में संख्याएँ किसी निश्चित नियम के अनुसार दी जाती हैं।
प्रश्न में आपको यह नियम पहचानकर अगला, गायब या गलत पद निकालना होता है।

2. How to Approach Number Series Questions (सवाल हल करने की विधि)

3. Common & Probable Types (सभी महत्वपूर्ण प्रकार)

Let’s go through every exam-relevant type with examples

Type 1 – Simple Arithmetic Progression (A.P.)

Rule: Fixed addition or subtraction.

Example:
3, 6, 9, 12, 15, ? → +3 → 18

In Hindi:
हर बार समान संख्या जोड़ी या घटाई जाती है।

Type 2 – Geometric Progression (G.P.)

Rule: Each term multiplied or divided by a fixed number.

Example:
2, 4, 8, 16, 32, ? → ×2 → 64

In Hindi:
प्रत्येक पद को किसी समान संख्या से गुणा या भाग किया जाता है।

Type 3 – Difference of Differences (Second Level Pattern)

Rule: First differences are not constant, but the difference of differences is constant.

Example:
2, 5, 10, 17, 26, ?
→ +3, +5, +7, +9 → Next = 26 + 11 = 37

Type 4 – Square / Cube Pattern

Rule: Series based on squares or cubes.

Examples:
1, 4, 9, 16, 25, ? → Squares → 36
1, 8, 27, 64, ? → Cubes → 125

Type 5 – Alternating Pattern

Rule: Two or more patterns alternate.

Example:
2, 4, 8, 16, 18, 36, 38, ?
→ (×2, +2 alternately) → 76

In Hindi:
दो अलग-अलग नियम बारी-बारी से लागू होते हैं।

Type 6 – Multiplication + Addition Pattern

Rule: Each term = previous term × n + constant.

Example:
3, 7, 15, 31, 63, ?
→ ×2 +1 pattern → 127

Type 7 – Prime Number Series (मूल संख्या श्रेणी)

Rule: Sequence of prime numbers or pattern involving primes.

Examples:
2, 3, 5, 7, 11, 13, ? → 17
Or 2, 5, 10, 17, 26, ? → +3, +5, +7, +9 → 37

Type 8 – Fibonacci / Recursive Pattern

Rule: Each term is sum (or difference) of previous two.

Examples:
1, 1, 2, 3, 5, 8, 13, ? → 21
2, 5, 7, 12, 19, ? → 7+12=19 → 31

Type 9 – Square Difference Series

Rule: Differences are perfect squares.

Example:
1, 2, 6, 15, 31, ?
→ Differences: +1, +4, +9, +16 → +25 → 56

Type 10 – Cube Difference Series

Example:
1, 9, 36, 100, 225, ?
→ Differences = 8, 27, 64, 125 → cubes → 216 → 441

Type 11 – Mixed Operations (+, –, ×, ÷)

Example:
2, 5, 10, 17, 26, ?
→ +3, +5, +7, +9 → 38

Type 12 – Odd-Even Position Pattern

Example:
3, 9, 5, 25, 7, 49, ?
→ Odd positions: +2 → 3,5,7,9
→ Even positions: squares of odd terms → 9,25,49,81 → Next = 9

Type 13 – Digit Reversal or Interchange Pattern

Example:
12, 21, 13, 31, 14, 41, ? → 15, 51

Type 14 – Wrong Number Series

Rule: Identify the number that doesn’t follow the pattern.

Example:
3, 6, 12, 24, 50, 96
→ ×2 pattern → wrong term = 50

Type 15 – Decimal / Fractional Series

Example:
1, 0.5, 0.25, 0.125, ? → ÷2 → 0.0625

Type 16 – Mixed Arithmetic & Geometric

Example:
2, 6, 18, 54, 162, ? → ×3 → 486

Type 17 – Square + Number Pattern

Example:
2, 5, 10, 17, 26, ?
→ +3, +5, +7, +9 → 38

Type 18 – Difference Based on Odd/Even Series

Example:
2, 3, 5, 8, 12, 17, ?
→ +1, +2, +3, +4, +5 → 23

Type 19 – Multiplication + Subtraction Pattern

Example:
3, 8, 23, 68, 203, ?
→ ×3 –1 → 608

Type 20 – Position or Place Value Logic

Example:
5, 10, 17, 26, 37, ?
→ Difference = 5,7,9,11 → +13 → 50

4. Identifying Pattern Quickly (ट्रिक से पहचानना)

5. Common Traps & Tips

✅ Always check difference first (most common).
✅ If not constant → check difference of differences.
✅ If numbers grow fast → check × or ÷ pattern.
✅ Alternate terms → odd/even pattern.
✅ Squares/Cubes up to 20 must be memorized.
✅ Write first few differences on paper → pattern emerges clearly.

6. Practice Examples

7. Quick Summary (संक्षेप में)

✅ Master Tip:
Always write first-level and second-level differences on paper; 80% of patterns become visible immediately.