Geometric series/geometric progression

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A geometric series is defined by its nth term formula, which can be used to derive specific terms. Given that the third term is 8 and the sixth term is 128, two equations can be established based on the formula. By solving these equations, the common ratio and the first term of the series can be determined. Understanding the properties of geometric progressions is crucial for solving such problems. The solution involves applying the nth term formula effectively to find the complete geometric series.
Elec68
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I can't figure this out for the life of me:

A geometric series exists with the third term of 8 and the sixth term of 128, what is the geometric series?
 
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Have you tried anything at all? What do you know about geometric series?
 
In particular, do you know the formula for the nth term of a geometric sequence? Use that formula knowing that a3= 8 and a6= 128 to get two equations in the two parameters you need.
 

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