+1042 When the same constant is added to the numbers 60, 120, and 160, a three-term geometric sequence arises. What is the common ratio of the resulting sequence?
+3400
When the same constant is added to the numbers 60, 120, and 160, a three-term geometric sequence arises.
What is the common ratio of the resulting sequence?
60 + x 120 + x
––––––– = –––––––
120 + x 160 + x
(120 + x) (120 + x) = (60 + x) (160 + x)
x2 + 240x + 14400 = x2 + 220x + 9600
240x – 220x = 9600 – 14400
20x = – 4800
x = – 240
60 – 240 120 – 240
–––––––––– = ––––––––––
120 – 240 160 – 240
– 180 – 120
–––––––––– = –––––––––– = 1.5
– 120 – 80
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