geometric mean?

Question

I have a problem which says , "the geometric mean of three distinct integers is 16".

does it mean that numbers itself are in geometric series ?

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Hi,

My question was different . i did not ask how to calculate G.M .

I asked , if i give you any 3 random integers and ask you to calculate a G.M , will that be a valid question ?

Or i should ask , hey , here i am giving you 3 integers which is in geometric series , now find a G.M for it ?

Which would be the valid question ?

see, in the first question i did not tell you whether the numbers are really in a geometric series or not .......thats a very important point and that was my question that in order to find a G.M whether the provided numbers has to be in a geometric series or not .

Answer 1

If three quantities are in Geometric Progression,the middle one is called the Geometric Mean of the other two
Thus 8.16 and 32 being in G.P.,16 is G.M.between 8 and 32
if however,any number of quantities are in GP ,all the terms between the first and last terms are called geometric mean between the first and the last terms.a,ar,ar^2,ar^3...ar^n,b are in GP,then ar,ar^2,,,,ar^n are the n geometric means between a and b

Answer 2

The geometric advise of two numbers, x and y, is given via geometric advise = sqrt(x*y) The mathematics advise of two numbers, x and y, is given via (x+y)/2 We additionally know that x+5=y So (x+x+5)/2 - a million/2 = sqrt(x*(x+5)) x + 2.5 - 0.5 = sqrt(x^2 + 5x) x + 2 = sqrt(x^2 + 5x) x^2 + 4x + 4 = x^2 +5x 4 = x because of the fact y = x+5, y = 9 So the two numbers are 4 and 9. The mathematics advise of four and 9 is (4+9)/2 = 6.5 (4+2.5 = 6.5 and six.5+2.5 = 9) The useful geometric advise of four and 9 is sqrt(4*9) = sqrt(36) = 6 (4 * a million.5 = 6 and six * a million.5 = 9) because of the fact the mathematics advise of 6.5 is a million/2 larger than the geometric advise of 6, this shows that we do certainly have the final solutions. i'm hoping this helps!

Answer 3

the geometric mean is done by multiplying all the numbers and then taking it to the root of the number of numbers N.
ex. 2,5,7 geometric mean would be cubed root of 2 X 5 X 7 or 70^1/3 power.

it is always smaller or equal to the arthmetic mean, it is only equal if all the numbers are the same.
Ex 5 X 5 X 5 X 5 ^ 1/4 = 5
remember take the square root if 2 numbers, cubed if 3, etc

Answer 4

BETTER TO SAY THESE NUMBERS WORK IN A GEOMETRIC SEQUENCE AND BE AWARE BECAUSE IT IS DIFERENT OF AN ARITMETIC SEQUENCE!!

Answer 5

yes it does

BETTER TO SAY THESE NUMBERS WORK IN A GEOMETRIC SEQUENCE AND BE AWARE BECAUSE IT IS DIFERENT OF AN ARITMETIC SEQUENCE!!