Say I have the numbers 2, 4, 8, 16. I want to find out a way to determine if this sequence is geometric without checking if 4/2=8/4=16/8. Is there are a formula that exists that would help with this?
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$\begingroup$As this is more or less the definition of a geometric sequence there is no other way to check it. Small variation are possible though as you could take the ratio of $4/2=2$ and then multiply it by each term to see if you get the next term given. This avoids repeated division but is essentially the same method, brute force.
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