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When the same constant is added to the numbers 60, 120, and 140, a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

 Jun 25, 2024
 #1
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(120 + x) / (60 + x)  = (140 + x) / (120 + x)

 

(120 + x) (120 + x) = (60 + x) (140 + x)

 

14400 + 240x + x^2  =  8400 + 200x + x^2

 

14400 - 8400  = 200x - 240x

 

6000 = - 40x

 

-6000/40 = x =  -150

 

The ratio is  [ 120 - 150 ] / [ 60 -150 ] =  [ -30] / -90 ] =   1 / 3

 

cool cool cool

 Jun 25, 2024

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