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:

Abolition Laws

Legislation aimed at ending the practice of slavery or the slave trade within a specific locale, region, or nation.

Indentured Servitude

A labor system where people paid for their passage to the New World by working for an employer for a fixed term of servitude, typically several years.

National Crime

Acts or offenses considered to be significantly harmful or dangerous to the interests or security of a nation, often punishable by law through the country's legal system.

Benjamin Rush

A Founding Father of the United States, who was a prominent physician, politician, social reformer, and educator, known for his contributions to American medicine and as a signer of the Declaration of Independence.