√3, 3, 3√3, …….. is 729?

Question

Which term of the G.P.

√3, 3, 3√3, …….. is 729?

Answer 1

Given G.P.: √3, 3, 3√3, …….. is 729 

a = √3, r = \(\frac{a_2}{a_1}\) = \(\frac{3}{\sqrt{3}}\) = √3 

now a_n = a . r^n-1 = 729 

⇒ (√3)(√3)^n-1 = 729 

⇒ (√3)ⁿ = 3⁶ = (√3)¹² 

⇒ n = 12 

So 12th term of GP √3, 3, 3√3, …….. is 729.