If 2 And 3 Are The Geomteric Mean Of M And N Find The Value Of M And N

If 2 and 3 are the geomteric mean of m and n find the value of m and n

 

Answer:

m = 4/3

n = 9/2

Step-by-step explanation:

If 2 and 3 are geometric means of m and n, then the sequence is:

m, 2, 3, n

Where:

a₁ = m

a₂ = 2

a₃ = 3

a₄ = n

Find the values of m and n using the ratio-proportion formula:

Common ratio, r = a₂/a₁ = a₃/a₂ = a₄/a₃

Find m:

2/m = 3/2

3m = (2)(2)

3m/3 = 4/3

m = 4/3

Find n:

n/3 = 3/2

2n = (3)(3)

2n/2 = 9/2

n = 9/2

Common ratio, r = 3/2

Check:

a₁ = 4/3

r = 3/2

a₂ = (4/3)(3/2)

a₂ = 2 (True)

a₃ = 2(3/2)

a₃ = 3  (True)

a₄ = 3(3/2)

a₄ = 9/2  (True)