Find the value of x for which x+9, x-6, 4 are the firs three terms of a G.P. and calculate the fourth term of the progression.

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x+9, x-6, 4 are terms in a G.P

==> x-6 = (x+9)*r ==> r= (x+9)/(x-6)

==> 4= (x-6)*r ==> r= 4/(x-6)

==> (x-6)^2 = 4(x+9)

==> x^2 - 12x + 36 = 4x + 36

==> x^2 -16x = 0

==> x(x-16) = 0

==> x1= 0

==> x2= 16

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x+9, x-6, 4 are terms in a G.P

==> x-6 = (x+9)*r ==> r= (x+9)/(x-6)

==> 4= (x-6)*r ==> r= 4/(x-6)

==> (x-6)^2 = 4(x+9)

==> x^2 - 12x + 36 = 4x + 36

==> x^2 -16x = 0

==> x(x-16) = 0

==> x1= 0

==> x2= 16

For x1= 0

==> r= 4/(x-6) = 4/6 = 2/3

==> a1= x+9 = 9

==> a2= 6

==> a3= 9*4/9= 4

==> a4= 9*8/27= 8/3

For x2= 16

==> r= 4/(x-6) = 4/10 = 2/5

==> a1= 16+9 = 25

==> a2= 25*2/5= 10

a3= 25*4/25 = 4

a4= 25*8/125 = 8/25

==>

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