UGC NET Paper 1 Unit 5 Topic 2: Mathematical Aptitude - Number series

🔢 UGC NET Paper 1 Unit 5 Number Series

🧠 Master arithmetic, geometric, and complex number patterns with this guide covering common differences, ratios, alternating series, and problem-solving strategies. Crucial for 3-5 NET questions per exam.

💡 Quick Summary: Number series problems test your ability to:

1. Identify patterns in numerical sequences
2. Predict next numbers in the series
3. Find missing numbers in given sequences

1. Arithmetic Series

🔹 Characteristics

• Constant difference between consecutive terms
• Formula: a_n = a₁ + (n-1)d
• Where:
  • a_n = nth term
  • a₁ = first term
  • d = common difference

🔹 Examples & Patterns

Type	Example	Pattern
Simple	2, 5, 8, 11, 14, ?	+3 each time (Answer: 17)
Decreasing	20, 17, 14, 11, 8, ?	-3 each time (Answer: 5)
Variable Difference	3, 6, 10, 15, 21, ?	Differences: +3, +4, +5, +6 (Answer: 28)

📌 Memory Aid: "ADD" for Arithmetic Series - Add Difference Directly

2. Geometric Series

Key Features:

• Constant ratio between consecutive terms
• Formula: a_n = a₁ × r^(n-1)
• Where:
  • r = common ratio

🔹 Types with Examples

Type	Example	Pattern
Simple	3, 6, 12, 24, 48, ?	×2 each time (Answer: 96)
Fractional Ratio	64, 32, 16, 8, 4, ?	÷2 each time (Answer: 2)
Squares/Cubes	1, 4, 9, 16, 25, ?	1², 2², 3², 4², 5² (Answer: 36)

🔹 Special Cases

1. Fibonacci: Each term is sum of two preceding terms (0, 1, 1, 2, 3, 5, 8...)
2. Prime Numbers: 2, 3, 5, 7, 11, 13, 17...
3. Triangular Numbers: 1, 3, 6, 10, 15 (sum of natural numbers)

3. Complex Series

Characteristics:

• Combination of different patterns
• Often requires multi-step analysis
• Common in NET exams

🔹 Common Complex Patterns

• Alternating Series: Two different patterns alternate
  Example: 2, 4, 3, 6, 5, 10, ? (Pattern: ×2, -1, ×2, -1... Answer: 9)
• Operation-Based: Different operations at each step
  Example: 5, 11, 19, 29, 41, ? (Pattern: +6, +8, +10, +12... Answer: 55)
• Digit-Based: Operations on digits of numbers
  Example: 12, 15, 21, 24, 30, ? (Pattern: sum of digits alternates 3 and 6... Answer: 33)

4. Problem Solving Strategies

Step	Action	Example
1. Observe	Look at the entire series	3, 7, 15, 31, 63, ?
2. Calculate Differences	Find differences between terms	Differences: +4, +8, +16, +32 (×2 pattern)
3. Check Ratios	Divide consecutive terms	Ratios: ~2.33, ~2.14, ~2.06, ~2.03 (approaching ×2)
4. Find Pattern	Identify the underlying rule	Pattern: ×2 +1 (Answer: 127)

🔥 Most Repeated NET Questions:

1. Next in series: 5, 16, 49, 104, ? (Answer: 181; Pattern: +11, +33, +55, +77)
2. Missing number: 2, 3, 5, 7, 11, ? (Answer: 13; Prime numbers)
3. Alternating series: 1, 2, 4, 7, 11, 16, ? (Answer: 22; Differences: +1, +2, +3...)
4. Complex pattern: 0, 4, 18, 48, 100, ? (Answer: 180; Pattern: n³-n²)
5. Geometric series: 1, 2, 6, 24, 120, ? (Answer: 720; Pattern: ×2, ×3, ×4, ×5, ×6)

📝 Common Mistakes to Avoid

🔹 Pitfalls in Number Series

Mistake	Explanation	Example
Overlooking Alternating Patterns	Missing that odd/even positions follow different rules	1, 1, 2, 3, 4, 7, 6, 15 (Odd: +1; Even: ×2 +1)
Ignoring Digit Operations	Not considering sum/product of digits	12, 15, 21, 24, 30 (Sum of digits alternates 3 and 6)
Premature Conclusion	Stopping after finding partial pattern	2, 4, 8, 16 (Could be ×2 or powers of 2 - need more terms)

🚀 Advanced Patterns

• Prime Factorization: Series based on prime factors
  Example: 6, 15, 35, 77, ? (Products of consecutive primes: 2×3, 3×5, 5×7, 7×11... Answer: 143)
• Position-Based: Terms related to their position
  Example: 1, 4, 27, 256, ? (nⁿ: 1¹, 2², 3³, 4⁴... Answer: 3125)
• Combination Series: Multiple operations combined
  Example: 1, 3, 6, 10, 15, ? (Triangular numbers: +2, +3, +4, +5... Answer: 21)

📌 Exam Tip: When stuck:

1. Calculate differences of differences (second differences)
2. Check if terms are sums/products of digits
3. Look for positional patterns (n², n³, etc.)
4. Consider alternating or multi-layer patterns

💡 Pro Strategy: Practice 5 series daily. Time yourself. Create your own series patterns to understand reverse logic!