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When the same constant is added to the numbers 60, 90, and 165, a three-term geometric sequence arises.  What is the common ratio of the resulting sequence?

 Jan 2, 2024
 #1
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(90 + d) / (60 + d)  = r , (165 + d) / (90 + d)  = r

 

Setting equal  for r  and simplifying

 

(90 + d)^2  = (60 + d) ( 165 + d)

 

d^2 + 180d + 8100 =  9900 + 225d + d^2

 

-45d = 1800

 

d = 1800 / -45  =  -40

 

r = [ 90 - 40 ] / [ 60 - 40 ] =  50 / 20   =  5/2

 

cool cool cool     

 Jan 2, 2024

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