Odd term in a factorial-like progression: 1, 1, 2, 6, 24, 96, 720 Exactly one number is inconsistent with n! progression.

Introduction / Context:Recognizing factorials is a staple skill in series: 0! = 1, 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720. A single non-factorial value stands out as the odd term.

Given Data / Assumptions:

• Given: 1, 1, 2, 6, 24, 96, 720.
• True factorials up to 6!: 1, 1, 2, 6, 24, 120, 720.

Concept / Approach:Match each term to n! for n = 0 through 6. The mismatch is the wrong number. Factorials grow rapidly; any off-by-one multipliers become obvious.

Step-by-Step Solution:1 = 0! (or 1!) ✓1 = 1! ✓2 = 2! ✓6 = 3! ✓24 = 4! ✓96 ≠ 5! (should be 120) ✗720 = 6! ✓

Verification / Alternative check:Since 96 = 24 * 4, while 5! must be 24 * 5, replacing 96 by 120 restores the perfect factorial sequence.

Why Other Options Are Wrong:

• 6 / 24 / 720 are exactly 3!, 4!, 6! and thus correct.

Common Pitfalls:

• Confusing powers (e.g., 4^3 = 64) with factorials; here only 96 is off.

Final Answer:96