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

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Answer 1 · 2017-12-31T01:32:13

A series of discrete points exponentially decreasing from 5 to approaching 0 by a factor of $1/2$

$a_n = 5(1/2)^(n-1)$

Assuming $n in NN$

This is the discrete set of points $a_n = 5/(2^(n-1))$

$a_n$ is an infinite geometric sequence with first term $(a_1) = 5$ and common ratio $(r) = 1/2$

Since $absr < 1$ we know that the sequence converges.

i.e $a_n->0$ as $n-> oo$

$:.$ We have a series of discrete points exponentially decreasing from 5 to approaching 0 by a factor of $1/2$

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

$a_1 =5, a_2=5/2, a_3 =5/4, a_4=5/8, a_5=5/16, a_6=5/32, ...$

enter image source here

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