math
posted by Mary .
What is the difference between geometric mean and arithmetic mean?
Arithmetic mean of two numbers A and B is:
(A + B)/2
Geometric mean of two numbers A and B is:
sqrt(A*B)
The geometric mean can be rewritten as follows:
sqrt(A*B) = Exp{Log[sqrt(A*B)]} =
Exp{1/2 [Log(A) + Log(B)]} =
Exp[Arithmetic mean of logarithms].
Respond to this Question
Similar Questions

geometric mean
The geometric mean of two postitive numbers a and b is sqrt(ab). Show that for f(x) = 1/x on any interval [a,b] of positive numbers, the value of c in the conclusion of the mean value theorem is c = sqrt(ab) I have no idea how to do … 
geometric mean
Eighteen is the Geometric Mean of 12 and what number 18 = sqrt (12 x) Solve for x. The answer is an integer, and it isn't 24 (That's the arithmetic mean). cheese is yellow 
Math *URGENT
Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646? 
arithmetic
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term … 
arithmetic
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term … 
math
The arithmetic mean of two numbers is 9 and their geometric mean is 3√5. Find these numbers 
ALGEBRA
the arithmetic mean of two numbers exceeds their geometric mean by two. find the numbers if one is 40 less than other? 
ALGEBRA
the arithmetic mean of two numbers exceeds their geometric mean by two. find the numbers if one is 40 less than the other? 
algebra
1. The geometric mean between the first two terms in a geometric sequence is 32. If the third term is 4, find the first term. 2. Insert a geometric mean between k and 1/k. 3. If 2 and 3 are two geometric means between m and n, fond … 
h.p.
the arithmetic mean of two numbers exceeds the geometric mean by 3/2 and geometric mean excceeds the harmonic mean by 6/5. find the numbers.