**lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y....**

### Question

lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y.### Options

A) 9/16

B) 3/4

C) 1

D) 4/3

E) 16/6

The correct answer is C.

### Explanation:

16/9, x, 1, y => a, ar, ar

ar

9 => r

ar

x xy = 4/3 x 3/4 = 1

^{2}, ar^{3}ar

^{2}= 1 => 16r^{2}/9 = 1 => 16r^{2}9 => r

^{2}= 9/16 => r = 3/4ar

^{2}= y = ar^{2}x r = 1 x 3/4 = 3/4x xy = 4/3 x 3/4 = 1

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16/9, x, 1, y => a, ar, ar

^{2}, ar^{3}ar

^{2}= 1 => 16r^{2}/9 = 1 => 16r^{2}9 => r

^{2}= 9/16 => r = 3/4ar

^{2}= y = ar^{2}x r = 1 x 3/4 = 3/4x xy = 4/3 x 3/4 = 1