Number series – fill the missing factorial term: 1, 1, 2, 6, 24, ?, 720 Recognize the factorial progression and supply the missing value.

Difficulty: Easy

Correct Answer: 120

Explanation:


Introduction / Context:
This is a classic factorial series. Recognizing factorial landmarks (1!, 2!, 3!, …) helps you recover missing terms instantly, a common pattern in aptitude tests.



Given Data / Assumptions:

  • List: 1, 1, 2, 6, 24, ?, 720.
  • Recall n! = 1*2*…*n, with 0! = 1 by convention.


Concept / Approach:
Map each term to factorials in order: 0!, 1!, 2!, 3!, 4!, 5!, 6!. The gap clearly corresponds to 5!.



Step-by-Step Solution:

0! = 11! = 12! = 23! = 64! = 245! = 120 → missing term6! = 720 → matches final term


Verification / Alternative check:
Continuity of factorial growth (rapidly increasing values) and exact match at 6! confirms correctness.



Why Other Options Are Wrong:

100/104/108 do not equal 5! and would break the strict factorial identity the sequence exhibits.


Common Pitfalls:
Confusing double factorial or powers for factorials; the given endpoints anchor factorial interpretation clearly.



Final Answer:
120

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