Find a Formula for the General Term $a _ { n }$

question 35

Short Answer

Find a formula for the general term $a _ { n }$ 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:

Inductive Generalization

A form of reasoning where a conclusion is drawn about all members of a group based on observations of a sample of that group.

Sodium

A chemical element with the symbol Na and atomic number 11, which is a soft, silvery-white, highly reactive metal and is found in many salts, including table salt.

Fallacies

Errors in reasoning that render arguments logically invalid, often due to misleading premises or irrelevant points.

Composition

The way in which something is made up or put together from various parts or elements.