A Sequenceis $\left\{ a _ { n } \right\}$ Defined Recursively by the Equation

question 36

Multiple Choice

A sequenceis $\left\{ a _ { n } \right\}$ defined recursively by the equation $a _ { n } = 0.5 \left( a _ { n - 1 } + a _ { n - 2 } \right)$ for $n \geq 3$ where $a _ { 1 } = 14 , a _ { 2 } = 14$ . Use your calculator to guess the limit of the sequence.

• A) 6
• B) 14
• C) 26
• D) 17
• E) 15

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Definitions:

Mental Lazy

A tendency to avoid cognitively demanding tasks, opting for simpler, less effortful thinking processes.

Motivation

The process of generating and expending energy toward achieving or avoiding some outcome.

Objective Facts

information verified to be true, independent of personal feelings, interpretations, or prejudice.

Role of Metaphor

The function metaphors serve in communication and thought, helping to convey complex ideas through comparative, symbolic language.