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When the same constant is added to the numbers $a,$ $b,$ and $c,$ a three-term geometric sequence arises. If $a = 60,$ $b = 100,$ and $c = 140,$ what is the common ratio of the resulting sequence?

 Jun 10, 2024
 #1
avatar+129733 
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Since the ratio between succesive terms is the same we  have

 

[100 +n ] / [ 60 + n]  = [ 140 + n ] / [ 100 + n ]     cross- multiply

 

[100 + n ] [ 100 + n ]  = [ 60 + n ] [140 + n]

 

10000 + 200n + n^2  =  8400 + 200n + n^2

 

10000   = 8400 

 

No solutions exist

 

cool cool cool

 Jun 10, 2024

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