Missing terms of a geometric seqeunce

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    Geometric Terms
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The discussion revolves around finding the missing terms in a geometric sequence starting with 3 and including the term 32x+1. The formula for the nth term of a geometric sequence, tn = ar^(n-1), is applied to derive the common ratio. The user simplifies the expression 32x+1 / 3 to find the common ratio, concluding that it equals 3x after further simplification. The conversation emphasizes the importance of simplifying expressions before taking square roots in geometric sequences. Ultimately, the user successfully identifies the missing terms with the help of hints provided.
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Homework Statement


Write the first 5 terms of the geometric sequence
3, __ , 32x+1, __, __

Homework Equations


tn=arn-1


The Attempt at a Solution


tn=arn-1
32x+1=3r3-1
r2=32x+1 / 3
r=√32x+1 / √3

I'm stuck
 
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Before taking the square root, try to simplyfy the right side. What is \frac{3^{2x+1}}{3^{1}}?
 
Hint:

If a,b,c are three consecutive terms of a geometric sequence, b^2 = ac.
 
Villyer said:
Before taking the square root, try to simplyfy the right side. What is \frac{3^{2x+1}}{3^{1}}?

Ohh I see. 32x+1 / 31 = 32x. And the square root of that is 3x.
Thank you
 

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