Find the alternative number to replace the question mark 1, 2, 6, 24, ?, 720

Concept: A sequence of factorials follows the rule an = n!, where n! (n factorial) means the product of all positive integers from 1 up to n — for example, 4! = 4 × 3 × 2 × 1 = 24. Recognizing this pattern lets any missing term of such a series be found directly by computing the matching factorial.

Application: Match each term of the given series 1, 2, 6, 24, ?, 720 to its factorial position:

1. 1st term = 1! = 1

2. 2nd term = 2! = 2 × 1 = 2

3. 3rd term = 3! = 3 × 2 × 1 = 6

4. 4th term = 4! = 4 × 3 × 2 × 1 = 24

5. 5th term (missing) = 5! = 5 × 4 × 3 × 2 × 1 = 120

6. 6th term = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Cross-check: Each factorial term equals the previous term multiplied by the next integer (n! = n × (n − 1)!). Using the confirmed 4th term (24) and 6th term (720): 24 × 5 = 120, and 120 × 6 = 720 — both check out, confirming the missing term.

Answer: The missing term is 120.