Write a Formula for the General Term (The Nth Term) $3,1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$

question 95

Multiple Choice

Write a formula for the general term (the nth term) of the geometric sequence.
- $3,1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots$

• A) \(a _ { n } = 3 \left( \frac { 1 } { 9 } \right) ^ { n - 1 }\)
• B) \(a _ { n } = 3 \left( \frac { 1 } { 3 } \right) ^ { n }\)
• C) \(\mathrm { a } _ { \mathrm { n } } = 3 \left( \frac { 1 } { 3 } \right) ^ { \mathrm { n } - 1 }\)
• D) \(a _ { n } = 3 \left( \frac { 1 } { 3 } \right) ^ { n + 1 }\)

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Definitions:

Carbanion

A negatively charged ion (anion) that consists of a carbon atom having a pair of non-bonded electrons.

Free Radical

Highly reactive atoms or molecules with an unpaired electron, involved in various chemical reactions.

Carbene

A highly reactive molecule featuring a carbon atom with two non-bonded electrons, making it very reactive.

Intermediates

Reactive species that are formed during the chemical reactions and lie in the reaction pathway between the reactants and the final products.