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in Geometric Progressions by (51.9k points)
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Insert 5 geometric means between 16 and 1/4.

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Let the five terms be a1, a2, a3, a4, a5.

A = 27, B = 1/81

Now, these 5 terms are between A and B.

So the GP is: A, a1, a2, a3, a4, a5, B.

So we now have 7 terms in GP with the first term being 16 and seventh being 1/4.

We know that, Tn = arn–1

Here, Tn = 1/4, a = 16 and

1/4 = 16r7-1

1/(4 × 16) = r6

r = 1/2

a1 = Ar = 16 × 1/2 = 8  

a2 = Ar2 = 16 × 1/4 = 4   

a3 = Ar3 = 16 × 1/8 = 2   

a4 = Ar4 = 16 × 1/16 = 1   

a5 = Ar5 = 16 × 1/32 = 1/2   

∴ The five GM between 16 and 1/4 are 8, 4, 2, 1, 1/2

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