Question

three geometric means between 3 and 48 are..?

Answer 1

let three geometric mean between 3 and 48 be A1,A2,A3
3,A1,A2,A3,48
48=3r⁴
r⁴=16
r=2
A1=3×2=6
A2=3×2²=3×4=12
A3=3×2³=8×3=24
therefore three geometric means are 6,12,24.

Answer 2

Three geometric means between 3 and 48 are 6 , 12 , 24 or - 6 , 12 , - 24

Given : The numbers are 3 and 48

To find : Three geometric means between 3 and 48

Solution :

Step 1 of 3 :

Assume the geometric means

Let a , b , c be three geometric means be inserted between 3 and 48

Then 3 , a , b , c , 48 forms a geometric progression

Let r be the common ratio

a = 3r

b = 3r²

c = 2r³

48 = 3r⁴

Step 2 of 3 :

Find the value of r

48 = 3r⁴

⇒ 3r⁴ = 48

⇒ r⁴ = 16

⇒ r = ± 2

Step 3 of 3 :

Find the geometric means

Taking r = 2

a = 6 , b = 12 , c = 24

Taking r = - 2

a = - 6 , b = 12 , c = - 24

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