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Logical Sequence

Logical Sequence problems present a sequence of numbers with one or more missing terms. You must identify the underlying pattern (arithmetic progression, geometric progression, square numbers, cube numbers, etc.) and determine the missing term. These problems test pattern recognition and mathematical reasoning skills.

10Worksheets
200+Practice Questions
Medium to HardDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Logical Sequence

Logical Sequence problems present a sequence of numbers with one or more missing terms. You must identify the underlying pattern (arithmetic progression, geometric progression, square numbers, cube numbers, etc.) and determine the missing term. These problems test pattern recognition and mathematical reasoning skills.

Prerequisites

Arithmetic progression understanding Geometric progression understanding Square and cube numbers Pattern recognition skills Basic algebra
Why This Matters: Logical Sequence problems appear in 2-3 questions in SSC CGL and Banking PO exams. They test pattern recognition and extrapolation skills.

How to Solve Logical Sequence Problems

1

Step 1: Write the sequence with position numbers

2

Step 2: Calculate differences between consecutive terms

3

Step 3: If differences are constant → arithmetic progression

4

Step 4: If ratios are constant → geometric progression

5

Step 5: If differences increase by constant amount → quadratic pattern

6

Step 6: Check if terms are perfect squares, cubes, or other special numbers

7

Step 7: Apply the pattern to find the missing term

8

Step 8: Verify the pattern works for all given terms

Pro Strategy: First check if the sequence is arithmetic (constant difference). If not, check if it's geometric (constant ratio). If neither, look for patterns in differences, or check if numbers are squares, cubes, primes, or follow a polynomial pattern.

Example Problem

Example: Find the missing number: 2, 4, 8, 16, ___ Solution: Step 1: Sequence: 2, 4, 8, 16, ? Step 2: Ratios: 4÷2=2, 8÷4=2, 16÷8=2 Step 3: Constant ratio = 2 (geometric progression) Step 4: Next term = 16 × 2 = 32 Answer: 32

Pro Tips & Tricks

  • Arithmetic: aₙ = a₁ + (n-1)d
  • Geometric: aₙ = a₁ × r^(n-1)
  • Square numbers: 1,4,9,16,25,36,49...
  • Cube numbers: 1,8,27,64,125,216...
  • Prime numbers: 2,3,5,7,11,13,17,19,23...
  • Fibonacci: each term = sum of previous two

Shortcut Methods to Solve Faster

If terms double each time → multiply by 2
If terms increase by adding 2,3,4,... → quadratic pattern
Check if terms are perfect squares (1,4,9,16...)
Check if terms are perfect cubes (1,8,27,64...)
Check if terms are prime numbers

Common Mistakes to Avoid

Assuming arithmetic without checking all differences
Forgetting that geometric sequences can have fractional ratios
Missing that the pattern could be alternating operations
Not verifying the pattern with all given terms

Exam Importance

Logical Sequence is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
INSURANCE
2-3 questions

Ready to Master Logical Sequence?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now