Factorial Series

Factorial Series problems consist of factorial numbers: 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720... These problems test knowledge of factorial values and ability to recognize factorial patterns.

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200+Practice Questions
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2-3 hoursHours to Master

Introduction to Factorial Series

Factorial Series problems consist of factorial numbers: 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720... These problems test knowledge of factorial values and ability to recognize factorial patterns.

Prerequisites

Factorial concept (n! = product of numbers 1 to n) Factorial values up to 10! Multiplication skills Exponential growth understanding
Why This Matters: Factorial Series problems appear in 0-1 questions in advanced exams like CAT and GMAT. They test knowledge of factorials.

How to Solve Factorial Series Problems

1

Step 1: List factorial values: 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720

2

Step 2: Compare given sequence with factorial values

3

Step 3: Identify pattern (consecutive factorials, factorials with offsets, etc.)

4

Step 4: For next term: find the next factorial value

5

Step 5: Verify that all terms follow the factorial pattern

6

Step 6: Present the next term

Pro Strategy: Memorize factorial values: 0! = 1, 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720, 7! = 5040, 8! = 40320, 9! = 362880, 10! = 3628800.

Example Problem

Example: Find the next term: 1, 2, 6, 24, ___ Solution: Step 1: Factorials: 1!=1, 2!=2, 3!=6, 4!=24 Step 2: Pattern: n! for n=1,2,3,4 Step 3: Next term = 5! = 120 Answer: 120

Pro Tips & Tricks

  • 0! = 1 (special case)
  • 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720
  • 7! = 5040, 8! = 40320, 9! = 362880, 10! = 3628800
  • Factorial grows very fast - answer will be large for n ≥ 5
  • Variation: n! + 1, n! - 1, (n+1)!, (n-1)!
  • Pattern may be aₙ = n! × k (multiply by constant)

Shortcut Methods to Solve Faster

Next factorial = last factorial × (n+1) where n is the last index
If term = n!, next = (n+1)! = n! × (n+1)
For n=5, 5! = 120, next 6! = 720 = 120 × 6
Factorial values: memorize up to 7! for quick recall

Common Mistakes to Avoid

Confusing factorial with exponent (2⁴=16 vs 4!=24)
Forgetting that 0! = 1 (not 0)
Using multiplication incorrectly (5! = 120, not 5×4×3×2=120? Actually that's correct)
Not recognizing that factorial series grow rapidly

Exam Importance

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

SSC CGL
0-1 questions
BANKING PO
0-1 questions
RAILWAYS RRB
0-1 questions
CAT
1-2 questions
GMAT
1-2 questions
INSURANCE
0-1 questions

Ready to Master Factorial Series?

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

20 practice questions
Detailed solutions
Step-by-step explanations
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