Which term of the G.P.√3, 3, 3√3, …….. is 729?

1.	Which term of the G.P.√3, 3, 3√3, …….. is 729?
Answer» 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.

Answer»

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.

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