SOLUTION: three numbers form a geometric progression if we double the middle number we get an arithematic progression the common ratio of the geomatric progression is ?
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Question 1037823: three numbers form a geometric progression if we double the middle number we get an arithematic progression the common ratio of the geomatric progression is ?
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
three numbers form a geometric progression if we double the middle number we get an arithmetic progression the common ratio of the geometric progression is ?
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Original Progression:: a, ar, ar^2
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New Progression:: a, 2ar, ar^2
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Common ratio:: Divide 2nd term by 1st to get:: (2ar)/a = 2r
Divide the 3rd term by the 2nd to get:: (ar^2)/(2ar) = r/2
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If 2r = r/2 , 4r = r
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Comment:: Your problem statement doesn't make much sense.
Cheers,
Stan H.
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Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.
three numbers form a geometric progression if we double the middle number we get an arithmetic progression.
the common ratio of the geometric progression is ?
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The original geometric progression: , , .
The new sequence is: , , .
The new progression is arithmetic. It means that - = - .
In other words, = .
Then = , --->
= ,
= (positive),
= (negative).
The previous solution was wrong.
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