SOLUTION: 5;x;y is an arithmetic sequence and x;y;81 is a geometric sequence.All terms in the sequence are integers.calculate the value of x and y.

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Question 1127067: 5;x;y is an arithmetic sequence and x;y;81 is a geometric sequence.All terms in the sequence are integers.calculate the value of x and y.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
A.S. 5, x, y
G.S. x, y, 81
Let d = the common difference of the A.S.
Thus:
x - 5 = d
y - x = d
y - 5 = 2d -> y - 5 = 2(x - 5) -> y = 2x - 5
So the terms of the G.S. are:
x, 2x - 5, 81
The common ratio r = (2x - 5)/x = 81/(2x - 5)
Solve for x:
(2x - 5)/x = 81/(2x - 5)
(2x - 5)^2 = 81x
4x^2 - 101x + 25 = 0
This can be factored as (4x - 1)(x - 25)
Since the terms are all integers, x = 25
Hence y = 2*25 - 5 = 45
Ans: x = 25, y = 45