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Question

If n geometric means be inserted between a and b then the nth geometric mean will be

A
a(ba)n(n1)
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B
a(ba)n1(n)
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C
a(ba)n(n+1)
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D
a(ba)1(n)
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Solution

The correct option is C a(ba)n(n+1)
If n geometric means g1,g2.....gn are to be inserted between two positive real numbers a and b, then a, g1,g2......gn, b are in G.P. Then
g1=ar,g2=ar2......gn=arn

So b=arn+1r=(ba)1/(n+1)
Now nth geometric mean (gn)=arn=a(ba)n/(n+1).
Aliter : As we have the mth G.M. is given by (Gm)=a(ba)n(n+1)
Now replace m by n we get the required result.

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