This is already answered by: Cerverusdante
So have the sequence: 1/5,2/15,4/45,8/135,16/405To check if the sequence is geometric, we are going to find its common ratio; to do it we are going to use the formula: r=(an)/(an-1)where r is the common ratio an is the current term in the sequence an is the previous term in the sequenceIn other words we are going to divide the current term by the previous term a few times, and we will to check if that ratio is the same:
For an= 2/15 and an-1=1/5 :r=(2/15)/(1/5)r=2/3
For an=4/45 and an-1=2/15:
r=(4/45)/(2/15)
r=2/3
For an=8/135 and an-1=4/45 :r=(8/135)/(4/45)
r=2/3
As you can see, we have a common ratio!
We can conclude that our sequence is a geometric sequence and its common ratio is 2/3
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