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Question

Let 3 geometric means G1,G2,G3 are inserted between two positive number a and b such that G3G2G2G1=2, then ba equal to

A
2
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B
4
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C
8
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D
16
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Solution

The correct option is B 2
Formulaused
Tn=arn1
Given
a,G1,G2,G3,binG.P
Letrbethecommonratio
G1=ar
G2=ar2
G3=ar3
b=ar4
Given
G3G2G2G1=2
ar3ar2ar2ar=2
ar2(r1)ar(r1)=2
r=2
Hence
b=ar4
=a(2)4
=16a
Hence
ba=16aa=16

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