If 1/3 ,m,1,n form a GP the product of m and n

Answer 1

To form a geometric progression (GP), we know that the ratio between any two consecutive terms must be the same.

Let's consider the given terms: 1/3, m, 1, n.

The ratio between the first and second terms is: m / (1/3) = 3m.

The ratio between the second and third terms is: 1 / m.

The ratio between the third and fourth terms is: n / 1 = n.

Since the ratio between the second and third terms is 1/m and the ratio between the third and fourth terms is n, we can equate them:

1/m = n

Solving for m, we get:

m = 1/n

Therefore, the product of m and n is:

m * n = (1/n) * n = 1

Answer 2

or, since 1 is the geometric mean of m and n,
√(mn) = 1
so mn = 1

Answer 3

Yes, you are correct. Since 1 is the geometric mean of m and n, we can also find the product of m and n by taking the square root of their product and setting it equal to 1.

√(mn) = 1

Squaring both sides:

mn = 1

Therefore, the product of m and n is indeed 1.