Given GP is √3, 3, 3√3….
The given GP is of the form, a, ar, ar2 , ar3….
Where r is the common ratio.
First term in the given GP,
a1 = a = √3
Second term in GP, a2 = 3
Now, the common ratio, \(r = \frac{a_2}{a_1}\)
r = \(\frac{3}{√3}\) = √3
Let us consider 729 as the nth term of the GP. Now, nth term of GP is, an = arn – 1
729 = √3 (√3)n – 1
√3n = √312
n = 12
So, 729 is the 12th term in GP.