If one Arithmetic Mean (A) and two Geometric Means (p,q) are inserted between two given numbers, show that

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- Nov 3rd 2010, 10:13 PMArkaProgression Prolem............
If one Arithmetic Mean (A) and two Geometric Means (p,q) are inserted between two given numbers, show that

- Nov 4th 2010, 04:52 AMHallsofIvy
Call the original numbers x and y. There arithmetic mean is . Strictly speaking, two numbers have only

**one**geometric mean but I think that you mean that x, p, q, y form a geometric progression. That would mean that p= xr, [tex]q= xr^2[tex] and . Dividing y by x, so that and so and .

Put those into and see if you get 2A= x+ y. - Nov 4th 2010, 10:51 AMArka
No I'm not getting x+y , if you are getting it then please show me the calculation......