+977 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?
+3320
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?
x + 60 x + 120
–––––––– = ––––––––
x + 120 x + 160
(x + 60)(x + 160) = (x +120)(x + 120)
x2 + 220x + 9600 = x2 + 240x + 14400
220x + 9600 = 240x + 14400
– 20x = 4800
x = – 240
– 240 + 60 – 240 + 120
––––––––––– = –––––––––––
– 240 + 120 – 240 + 160
– 180 – 120 3
–––––– = –––––– = –––
– 120 – 80 2
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