Question

If three geometric means be inserted between 2 and 32, then the third geometric mean will be

Answer 1

If three geometric means be inserted between 2 and 32, then the third geometric mean will be - 16 or 16

Given : Three geometric means be inserted between 2 and 32

To find : The third geometric mean

Solution :

Step 1 of 3 :

Assume the geometric means

Let a , b , c be three geometric means be inserted between 2 and 32

Then 2 , a , b , c , 32 forms a geometric progression

Let r be the common ratio

a = 2r

b = 2r²

c = 2r³

32 = 2r⁴

Step 2 of 3 :

Find the value of r

32 = 2r⁴

⇒ 2r⁴ = 32

⇒ r⁴ = 16

⇒ r = ± 2

Step 3 of 3 :

Find the geometric means

Taking r = 2

a = 4 , b = 8 , c = 16

Taking r = - 2

a = - 4 , b = 8 , c = - 16

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