Geometric Series: Find 3 Numbers for 5 Components

AI Thread Summary
To find three numbers that form an increasing geometric series with five components between 31 and 496, the common ratio (q) must be correctly identified. The user initially miscalculated by adding instead of multiplying, which is essential in geometric sequences. The correct approach involves using the formula where each term is derived by multiplying the previous term by q. Clarification on the multiplication method helped the user understand their mistake. The discussion emphasizes the importance of applying the correct mathematical operations in geometric series problems.
Femme_physics
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Homework Statement



You must enter 3 numbers between 31 and 496 so there will be an increasing geometric series with 5 components.


The Attempt at a Solution



It tells me I'm off. That q=2. But how?

http://img716.imageshack.us/img716/8895/300xk.jpg
 
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Hey FP :)

Multiply instead of add?
 
With a geometric series, you multiply by q to get successive terms:

\begin{align*}<br /> a_2 &amp; = a_1 q \\<br /> a_3 &amp; = a_1 q^2 \\<br /> a_4 &amp; = a_1 q^3 \\<br /> a_5 &amp; = a_1 q^4<br /> \end{align*}

Do you see your mistake now?
 
I like Serena said:
Hey FP :)

Multiply instead of add?


w00t! :) I hope I have all the formulas at the test so I can relook them. Thanks, ILS! And vela, too :)
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...

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