Bode's Sequence, Defined By $a _ { 1 } = 0.4 , a _ { k } = 0.1 \left( 3 \cdot 2 ^ { k - 2 } + 4 \right) \text { for } k \geq 2$

question 13

Multiple Choice

Bode's sequence, defined by $a _ { 1 } = 0.4 , a _ { k } = 0.1 \left( 3 \cdot 2 ^ { k - 2 } + 4 \right) \text { for } k \geq 2$ can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 5th term of the sequence.

• A) \(a _ { 5 } = 4.1\)
• B) \(a _ { 5 } = 2.3\)
• C) \(a _ { 5 } = 3.2\)
• D) \(a _ { 5 } = 2.8\)
• E) \(a _ { 5 } = 6.8\)

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Definitions:

Monopolistically Competitive Industry

A market structure where many firms sell products that are similar but not identical, allowing for significant differentiation and non-price competition.

Perfectly Competitive Industry

An industry characterized by many small firms producing identical products where no single firm can influence the market price.

Advertising Expenditures

The amount of money spent on promoting products, services, or brands through various media channels.

Price Discrimination

A method of setting prices in which the same provider sells nearly the same goods or services at disparate prices in different markets.