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:

Information-processing Ability

The capacity of the brain to analyze, evaluate, and retain information, helping in decision-making and problem-solving.

Causality

The relationship between cause and effect, where one event (the cause) directly influences the outcome of another event (the effect).

Innate Learning

Refers to the natural capability to understand and process information from birth, suggesting some knowledge or skills are not acquired but inherent.

Information Processing

A cognitive approach that considers how individuals encode, store, and retrieve information almost like a computer processing data.