How do you tell whether the sequence #2, 4, 8, 16, 32# is arithmetic?

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Answer 1 · 2017-07-04T13:25:15

This is not an arithmetic sequence, it is a geometric sequence

Let's call the terms of the series

#u_1=2#

#u_2=4#

#u_3=8#

#u_4=16#

#u_5=32#

To see if the sequence is arithmetic, we calculate

#u_n-u_(n-1)#

If this is constant, we have an arithmetis sequence

#u_5-u_4=32-16=16#

#u_4-u_3=16-8=8#

#u_3-u_2=8-4=4#

#u_2-u_1=4-2=2#

This is not constant, so this is not an arithmetic sequence.

But, we can check to see if it's a geometric sequence

We calculate #u_n/u_(n-1)#

#u_5/u_4=32/16=2#

#u_4/u_3=16/8=2#

#u_3/u_2=8/4=2#

#u_2/u_1=4/2=2#

So this is a geometric sequence of general term

#u_n=2^n#