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When the same constant is added to the numbers 60, 100, and 180, a three-term geometric sequence arises.  What is the common ratio of the resulting sequence?

 

 

\(\phantom{60, 100, and 160}\)

 Jun 22, 2022
 #1
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(100 + N)  / (60+N)      =  (180 + N) / (100 + N)

 

(100 + N)^2  =  (180 + N) (60 + N)

 

10000 + 200N  + N^2  =  10800 + 240N + N^2

 

200N - 240N =  10800  - 10000

 

-40N  =  800

 

N =  800 / -40  =   -20 

 

Common Ratio   =  (100 -20) / (60 - 20)  =  80 / 40   =   2

 

 

 

cool cool cool

 Jun 22, 2022

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