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in Geometric Progressions by (15.2k points)

Which term of the GP√3, 3, 3√3… is 729?

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1 Answer

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by (15.7k points)

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.

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