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:

Psychological Theories

Systematic frameworks for understanding human behavior and mental processes.

Observed Facts

Information and data obtained through direct observation or measurement, not influenced by interpretations or assumptions.

Generate Hypotheses

The process of forming statements or predictions that can be tested to explore a potential outcome or phenomenon.

Hindsight Bias

The tendency to believe, after learning an outcome, that one would have foreseen it, also known as the "knew-it-all-along" effect.