Find The $n ^ { \text {th } }$ Term of the Sequence Whose First Several Terms Are

question 38

Multiple Choice

Find the $n ^ { \text {th } }$ term of the sequence whose first several terms are $\frac { 1 } { 4 } , - \frac { 1 } { 9 } , \frac { 1 } { 16 } , - \frac { 1 } { 25 } , \ldots$

• A) \(a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { n ^ { 2 } }\)
• B) \(a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { ( n + 1 ) ^ { 2 } }\)
• C) \(a _ { \mathrm { n } } = \frac { ( n + 1 ) ^ { n } } { 4 ^ { 2 } }\)
• D) \(a _ { n } = \frac { ( 1 ) ^ { n } } { ( 2 n ) ^ { 2 } }\)
• E) none of these

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Definitions:

Hierarchy

An arrangement or institution where individuals or entities are classified above or below each other based on their status or power.

Organizational Behavior

The study of individual and group dynamics within an organizational context, focusing on improving productivity and promoting healthy work environments.

Real-life Settings

Contexts or environments that occur naturally in everyday life, as opposed to controlled or artificial situations.

Evidence-based Management

The practice of making managerial decisions based on the best available scientific evidence and data.