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. $$\left\{ - \frac { 1 } { 2 } , \frac { 16 } { 3 } , - \frac { 81 } { 4 } , \frac { 256 } { 5 } , - \frac { 625 } { 6 } , \ldots \right\}$$

---

Definitions:

Relationship Longevity

The duration and persistence of a social connection, partnership, or marriage over time.

Dark Triad

A grouping of three personality traits: narcissism, Machiavellianism, and psychopathy, which are associated with a manipulative, exploitative, and socially aversive behavior.

Psychopathy

A disorder of the personality marked by ongoing antisocial actions, a lack of empathy, alongside bold, uninhibited, and self-centered characteristics.

Machiavellianism

A personality trait that sees a person so focused on their own interests they will manipulate, deceive, and exploit others to achieve their goals.