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+1⇒r=(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.