# How do you graph a_n=5(1/2)^(n-1)?

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Alan N. Share
Dec 31, 2017

A series of discrete points exponentially decreasing from 5 to approaching 0 by a factor of $\frac{1}{2}$

#### Explanation:

${a}_{n} = 5 {\left(\frac{1}{2}\right)}^{n - 1}$

Assuming $n \in \mathbb{N}$

This is the discrete set of points ${a}_{n} = \frac{5}{{2}^{n - 1}}$

${a}_{n}$ is an infinite geometric sequence with first term $\left({a}_{1}\right) = 5$ and common ratio $\left(r\right) = \frac{1}{2}$

Since $\left\mid r \right\mid < 1$ we know that the sequence converges.

i.e ${a}_{n} \to 0$ as $n \to \infty$

$\therefore$ We have a series of discrete points exponentially decreasing from 5 to approaching 0 by a factor of $\frac{1}{2}$

To graph such a sequence you could plot a series of discrete points as below:

${a}_{1} = 5 , {a}_{2} = \frac{5}{2} , {a}_{3} = \frac{5}{4} , {a}_{4} = \frac{5}{8} , {a}_{5} = \frac{5}{16} , {a}_{6} = \frac{5}{32} , \ldots$

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