Number series (find the wrong term): 1, 1, 2, 6, 24, 96, 720 Identify the single term in the sequence that does not fit the underlying pattern. Explain your reasoning clearly.

Introduction / Context:Number-series questions test the ability to spot a hidden rule. Here the sequence resembles the classic factorial pattern often used in aptitude and competitive exams. We must locate the single term that violates the rule.

Given Data / Assumptions:

• Series: 1, 1, 2, 6, 24, 96, 720
• Exactly one term is wrong.
• No missing terms; we are to find the misfit.

Concept / Approach:Recognize factorials: n! equals the product 123*…*n. The standard factorial sequence is 1 (0!), 1 (1!), 2 (2!), 6 (3!), 24 (4!), 120 (5!), 720 (6!). Compare each given term against this benchmark.

Step-by-Step Solution:Compare first five terms: 1, 1, 2, 6, 24 match 0!, 1!, 2!, 3!, 4! respectively.The sixth term should be 5! = 120, but the series shows 96.The seventh term 720 matches 6! = 720.Therefore, 96 is the single misfit; it should have been 120 to remain a proper factorial series.

Verification / Alternative check:Reconstruct the corrected series: 1, 1, 2, 6, 24, 120, 720. All terms now follow n! strictly and increase as expected.

Why Other Options Are Wrong:

• 2, 6, 24, 720: Each exactly equals 2!, 3!, 4!, and 6! respectively; these are correct.
• 96: Not equal to any factorial; this breaks the pattern.

Common Pitfalls:Candidates sometimes assume a multiplication-by-integers rule but forget the factorial definition. Another mistake is to treat 1 as only 1!, ignoring 0! = 1, which also fits the sequence.

Final Answer:96