Find the missing term in the factorial pattern: 1, 1, 2, 6, 24, ?, 720

Introduction / Context:This is a sequence recognition question. The numbers resemble factorials, which are products of all positive integers up to a given n. Recognizing the pattern lets us supply the missing term.

Given Data / Assumptions:

• Sequence: 1, 1, 2, 6, 24, ?, 720.
• Consecutive terms increase rapidly, suggesting factorial growth.

Concept / Approach:Recall factorial definition: n! = 1 * 2 * 3 * ... * n. Note small factorials: 0! = 1, 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720. Map these to the given sequence to identify the missing value.

Step-by-Step Solution:Identify terms: 1 (0!), 1 (1!), 2 (2!), 6 (3!), 24 (4!), ? (5!), 720 (6!).Thus the missing term is 5! = 120.

Verification / Alternative check:Compute 6! = 720 matches the last term, confirming factorial interpretation and validating 5! = 120 as the missing entry.

Why Other Options Are Wrong:

• 100, 104, 108, 144: None are equal to 5! and do not fit the factorial pattern.

Common Pitfalls:

• Forgetting that both 0! and 1! equal 1, which explains the first two terms.

Final Answer:120