# Three positive numbers form a geometric sequence. if the geometric mean of two numbers is 6 and the geometric mean of the last two terms is 24, find the three numbers and their common ratio

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by YummyPicks

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by YummyPicks

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√(A₂ x A₃) = 24

*Transform both equations so that A₂ will be left on one side.

*Square both sides then divide by A₁/A₃

A₂= 36/A₁

A₂= 576/A₃

therefore,

36/A₁ = 576/A₃

*Going back to the fomula for finding An

A₃=A₁r²

*Substitute

36/A₁ = 576/A₁r²

*Multiply both sides by A₁r²

36r² = 576

r² = 16

r=+/- 4

*Since al terms are positive then tha common ratio is 4.

*The geometric mean of the two given numbers would be the second term which is 12. by that, you can tel what are the three terms.

3, 12, 48