Write an Expression for the N Th Term of the Sequence

question 53

Multiple Choice

Write an expression for the n th term of the sequence $1,3 , \frac { 3 ^ { 2 } } { 2 } , \frac { 3 ^ { 3 } } { 6 } , \frac { 3 ^ { 4 } } { 24 } , \frac { 3 ^ { 5 } } { 120 } , \ldots$ Assume that n begins with 1.

• A) \(a _ { n } = \frac { 3 ^ { n - 1 } } { n ! }\)
• B) \(a _ { n } = \frac { 3 ^ { n + 1 } } { ( n - 1 ) ! }\)
• C) \(\alpha _ { n } = \frac { 3 ^ { n } } { ( n - 1 ) ! }\)
• D) \(a _ { n } = \frac { 3 ^ { n } } { n ! }\)
• E) \(\alpha _ { n } = \frac { 3 ^ { n - 1 } } { ( n - 1 ) ! }\)

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Definitions:

Emergent Layer

The topmost layer of a rainforest, where the tallest trees extend above the forest's general canopy, receiving most sunlight.

Species Diversity

The variety and abundance of different species within a given area, crucial for ecosystem health and resilience.

Terrestrial Biomes

Large geographic regions defined by the dominant plant life and climate, including forests, deserts, grasslands, and tundra.