# math

posted by .

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].

## Similar Questions

1. ### 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 …
2. ### 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
3. ### 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?
4. ### 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 …
5. ### 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 …
6. ### math

The arithmetic mean of two numbers is 9 and their geometric mean is 3√5. Find these numbers
7. ### ALGEBRA

the arithmetic mean of two numbers exceeds their geometric mean by two. find the numbers if one is 40 less than other?
8. ### ALGEBRA

the arithmetic mean of two numbers exceeds their geometric mean by two. find the numbers if one is 40 less than the other?
9. ### 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 …
10. ### 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.

More Similar Questions