√(A₁ x A₂) = 6
√(A₂ x A₃) = 24
*Transform both equations so that A₂ will be left on one side.
*Square both sides then divide by A₁/A₃
36/A₁ = 576/A₃
*Going back to the fomula for finding An
36/A₁ = 576/A₁r²
*Multiply both sides by A₁r²
36r² = 576
r² = 16
*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