Find the Nth Term $a _ { n }$ Of a Sequence Whose First Four Terms Are Given

question 37

Multiple Choice

Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
- $$\frac { 5 } { 16 } , \frac { 10 } { 25 } , \frac { 15 } { 36 } , \frac { 20 } { 49 } , \ldots$$

• A) \(a _ { n } = \frac { 5 ^ { n } } { ( n + 3 ) ^ { 2 } }\)
• B) \(a _ { n } = \frac { 5 n } { ( n + 2 ) ^ { 2 } }\)
• C) \(a _ { n } = \frac { 5 ^ { n } } { ( n + 2 ) ^ { 2 } }\)
• D) \(a _ { n } = \frac { 5 n } { ( n + 3 ) ^ { 2 } }\)

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Definitions:

Generations

Groups of individuals categorically divided based on their birth years, sharing similar social, cultural, political, and economic influences.

Big Data

Large volumes of data that can be analyzed computationally to reveal patterns, trends, and associations, especially relating to human behavior and interactions.

Volume

The quantity of something, measured in terms of units, such as sales volume, which refers to the number of units sold within a particular period.

Research Design

A systematic plan outlining how a research project is conducted, including the methods and procedures used to collect and analyze data.