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

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Alan N. Share
Dec 31, 2017

Answer:

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

Explanation:

#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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