Find the Fifth Term and the Nth Term of the Geometric

question 2

Multiple Choice

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
- $$\mathrm { a } = 2 ; \mathrm { r } = 3$$

• A) \(a _ { 5 } = 162 ; a _ { n } = 2 \cdot ( 3 ) ^ { n - 1 }\)
• B) \(\mathrm { a } _ { 5 } = 486 ; \mathrm { a } _ { \mathrm { n } } = 2 \cdot ( 3 ) ^ { \mathrm { n } }\)
• C) \(a _ { 5 } = 162 ; a _ { n } = 2 \cdot ( 3 ) ^ { n }\)
• D) \(a _ { 5 } = 486 ; a _ { n } = 2 \cdot ( 3 ) ^ { n - 1 }\)

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Definitions:

1-Propanol

An alcohol with the formula C3H7OH, used as a solvent and an intermediate in the production of other chemicals.

Sodium Acetylide

A chemical compound formed by the reaction of acetylene with sodium metal, used in organic synthesis.

Hexanal

An organic compound with the formula C6H12O, known as an aldehyde due to its terminal carbonyl group, and commonly found in the aroma of freshly cut grass.

Acid Chloride

A functional group in organic chemistry, characterized by a carbon atom double-bonded to an oxygen atom and bonded to a chlorine atom.