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The sequence $4 ; x ; y ; 18$ is such that $4 ; x ; y$ form an arithmetic sequence and $x,y$ and 18 form a geometric sequence

1. Using the common difference of the arithmetic sequence, determine $y$ in terms of $x$
2. Using the common ratio of the geometric sequence, determine $y$ in terms of $x$
3. Hence, or otherwise, calculate the value(s) of $x$ and $y$

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1. x-4=y-x

y=2x-4

2. y/x = 18/y

y^2 = 18x

y= sqroot(18x)

3. y=2x-4

sqroot(18x)=2x-4

18x= (2x-4)^2

4x^2 -34x+16=0

2x^2 -17x+8=0

(2x-1)(x-8)=0

x= 1/2 or 8

then y= 2(1/2)-4= -3  or y= 2(8)-4=12
by Diamond (44,680 points)

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