SOLUTION: Find x if the sequence 8, x, (5/2)x is geometric. How is this done?

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Question 1034286: Find x if the sequence 8, x, (5/2)x is geometric. How is this done?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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I see here three terms that are not part of a geometric sequence.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Find x if the sequence 8, x, (5/2)x is geometric. How is this done?
With this being a GP, we EQUATE terms as follows: matrix%281%2C2%2C+2%5E%28nd%29%2C+term%29%2Fmatrix%281%2C2%2C+1%5E%28st%29%2C+term%29%22=%22matrix%281%2C2%2C+3%5E%28rd%29%2C+term%29%2Fmatrix%281%2C2%2C+2%5E%28nd%29%2C+term%29.

We then get:

x%2F8+=+%285%2F2%29x%2Fx

x%2F8+=+%285x%2F2%29%2Fx

matrix%281%2C3%2C+x%2F8+=+5x%2F2%2C+%22%F7%22%2C+x%29

matrix%281%2C3%2C+x%2F8+=+5x%2F2%2C+%22%2A%22%2C+1%2Fx%29

matrix%281%2C3%2C+x%2F8+=+5cross%28x%29%2F2%2C+%22%2A%22%2C+1%2Fcross%28x%29%29

x%2F8+=+5%2F2

2x = 40 ------- Cross-multiplying

highlight_green%28matrix%281%2C3%2C+x+=+40%2F2%2C+or%2C+x+=+20%29%29



Hence, this is a GP, with a%5B1%5D+=+8, and matrix%281%2C8%2C+r%2C+or%2C+common%2C+ratio%2C+%22=%22%2C+20%2F8%2C+or%2C+2.5%29