Geometric Progression What is the value of x and y if 2, x, y, 16 form a geometric progression ?

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Consecutive terms of a GP have a common ratio. if 2, x, y, 16 form a GP.

=> 16/y = x/2

=> x = 32/y

y/x = x/2

Substitute x = 32/y

=> y/(32/y) = (32/y)/2

=> 2y = (32/y)^2

=> 2y^3 = 32^2

=> y^3 = 32^2/2

=> y^3...

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Consecutive terms of a GP have a common ratio. if 2, x, y, 16 form a GP.

=> 16/y = x/2

=> x = 32/y

y/x = x/2

Substitute x = 32/y

=> y/(32/y) = (32/y)/2

=> 2y = (32/y)^2

=> 2y^3 = 32^2

=> y^3 = 32^2/2

=> y^3 = 2^(10 - 1)

=> y^3 =  2^9

=> y^3 = 8^3

=> y = 8

x = 32/y = 4

The value of x = 4 and y = 8

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