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When the same constant is added to the numbers 60, 100  and 165 a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

 Apr 9, 2024
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We can solve this

 

[100 + x ]  / [ 60 + x] =  [ 165 + x ] / [100 + x]

 

[100 + x]^2 = [ 60 + x ] [ 165 + x ]

 

x^2 + 200x + 10000 =  x^2 + 225x + 9900

 

10000 - 9900  =  25x

 

100 =  25x

 

x =  100 /  25  =  4

 

Check

 

104 / 64 = 13 / 8

 

169 / 104  =  13 / 8

 

r  =13 / 8

 

cool cool cool

 Apr 9, 2024

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