SOLUTION: The product and sum of three consecutive terms in a Geometric Progression are 3375 and 65 respectively. Find the difference between the largest and smallest terms of the three numb

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Question 807576: The product and sum of three consecutive terms in a Geometric Progression are 3375 and 65 respectively. Find the difference between the largest and smallest terms of the three numbers
Answer by stanbon(75887) About Me  (Show Source):
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The product and sum of three consecutive terms in a Geometric Progression are 3375 and 65 respectively. Find the difference between the largest and smallest terms of the three numbers
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Product: (a*ar*ar^2) = 3375
(ar)^3 = 3375
ar = 15
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Sum::::: (a + ar + ar^2) = 65
(a + ar + ar*r) = 65
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Substitute for ar in the sum to get
(a + 15 + 15r) = 65
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Two Equations::
ar = 15
a + 15r = 50
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Substitute for "a" and solve for "r":
(50-15r)r = 15
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15r^2 - 50r + 15 = 0
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3r^2 - 10r + 3 = 0
Factor:
3r^2-9r-r+3 = 0
3r(r-3)-(r-3) = 0
(r-3)(3x-1) = 0
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r = 3 or r = 1/3
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If r = 3, a = 5 : Then ar^2 = 45:: Then difference = 45-5 = 40
If r = 1/3, a = 45: Then ar^2 = 5:: Then diffeerence = 5-45 = -40
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Cheers,
Stan H.
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