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Question

If n geometric means between a and b be G1,G2,.......Gn and a geometric mean be G, then the true relation is

A
G1.G2.......Gn=G
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B
G1.G2.......Gn=G1/n
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C
G1.G2.......Gn=Gn
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D
G1.G2.......Gn=G2/n
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Solution

The correct option is C G1.G2.......Gn=Gn
Here G=(ab)1/2 and G1=ar1,G2=ar2,......Gn=arn
Therefore G1.G2.G3......Gn=anr1+2+....+n=anrn(n+1)/2
But arn+1=br=(ba)1/(n+1)
Therefore, the required product is
an(ba)1/(n+1).n(n+1)/2=(ab)n/2={(ab)1/2}n=Gn.


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