Find a Formula for the General Term of the Sequence $$\left\{ - \frac { 1 } { 2 } , \frac { 16 } { 3 } , - \frac { 81 } { 4 } , \frac { 256 } { 5 } , - \frac { 625 } { 6 } , \ldots \right\}$$

question 38

Short Answer

Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues. $$\left\{ - \frac { 1 } { 2 } , \frac { 16 } { 3 } , - \frac { 81 } { 4 } , \frac { 256 } { 5 } , - \frac { 625 } { 6 } , \ldots \right\}$$

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Definitions:

Conscientiousness

A personality trait characterized by diligence, carefulness, and a desire to do a task well.

Filial Loyalty

The devotion, duty, and respect that a child typically shows towards their parents.

East Asian Culture

encompasses the customs, traditions, and social values of countries in East Asia, including China, Japan, Korea, and others, often emphasizing harmony, respect, and community.

Confucian Ideals

Ethical teachings and philosophies based on the teachings of Confucius, emphasizing virtues such as respect, sincerity, and filial piety.