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JH

# (a) A sequence $\left\{ a_n \right\}$ is defined recursively by the equation $a_n = \frac {1}{2} \left(a_{n - 1} + a_{n - 2} \right)$ for $n \ge 3,$ where $a_1$ and $a_2$ can be any real numbers. Experiment with various values of $a_1$ and $a_2$ and use your calculator to guess the limit of the sequence.(b) Find $\lim_{n \to \infty} a_n$ in terms of $a_1$ and $a_2$ by expressing $a_{n + 1} - a_n$ in terms of $a_2 - a_1$ and summing a series.

## (A). Seems to approach $\frac{2}{3}$ of the way from al to a2(B). $\frac{a_{1}}{3}+\frac{2 a_{2}}{3}$

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University of Michigan - Ann Arbor

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University of Nottingham

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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Join Bootcamp