A Recursion Formula and the Initial Term(s) of a Sequence $a _ { 1 } = 1 , a _ { n + 1 } = \frac { a _ { n } } { n + 2 }$

question 403

Multiple Choice

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
- $a _ { 1 } = 1 , a _ { n + 1 } = \frac { a _ { n } } { n + 2 }$

• A) \(1 , \frac { 1 } { 3 } , \frac { 3 } { 4 } , \frac { 4 } { 5 } , \frac { 5 } { 6 }\)
• B) \(1 , \frac { 1 } { 3 } , 12 , \frac { 1 } { 60 } , 360\)
• C) \(1 , \frac { 1 } { 3 } , \frac { 1 } { 12 } , \frac { 1 } { 60 } , \frac { 1 } { 360 }\)
• D) \(1 , \frac { 1 } { 3 } , \frac { 1 } { 4 } , \frac { 1 } { 5 } , \frac { 1 } { 6 }\)

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Definitions:

Ecological Isolation

A form of reproductive isolation where different species live in the same area but occupy different habitats, preventing them from mating and producing offspring.

Balanced Dimorphisms

The occurrence of two different forms or morphs of a species in the same population, maintained in a stable equilibrium through natural selection.

Population

A group of individuals of the same species living and interbreeding within a given area.

Illustration

A visualization or a depiction made by an artist, such as a drawing or painting, that complements, elucidates, or decorates text.