Write an Expression for the Apparent Nth Term of the Sequence.(Assume

question 39

Multiple Choice

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1. ) ​ $$\frac { 2 } { 7 } , \frac { 3 } { 15 } , \frac { 4 } { 23 } , \frac { 5 } { 31 } , \frac { 6 } { 39 } , \ldots$$ ​

• A) \(a _ { n } = \frac { n + 1 } { 8 n - 8 }\)
• B) \(a _ { n } = \frac { n - 1 } { 8 n + 1 }\)
• C) \(a _ { n } = \frac { n + 1 } { 8 n + 1 }\)
• D) \(a _ { n } = \frac { n - 1 } { 8 n - 1 }\)
• E) \(a _ { n } = \frac { n + 1 } { 8 n - 1 }\)

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Definitions:

Aromatic

Refers to a class of compounds that contain a benzene ring or a similar structure with delocalized electrons that follow Huckel's rule.

AntiAromatic

Compounds that have conjugated pi electron systems with 4n pi electrons, which destabilize the molecule, making it less stable than if the pi electrons were localized.

NonAromatic

Refers to organic compounds that do not possess the special stability associated with cyclic, planar systems that follow Huckel’s rule of delocalized electrons.

π Network

A system of conjugated pi bonds within a molecule that allows for the delocalization of pi electrons across all the adjacent aligned p orbitals.