Question

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 $y$

 

Answer 1

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