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

question 21

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:

Mean Age

The mean age of a specific group or population, determined by adding together the ages of all members and then dividing by the total number of members.

Heights of Men

The distribution of vertical measurements of adult males in a specific population or group.

Standard Deviation

A parameter reflecting the extent of diversity or spread in a group of numbers.

Normally Distributed

A type of distribution in which data points are symmetrically distributed around the mean, forming a bell-shaped curve.