Question

The sum of 8 terms of G.P. 1 , √ , 3 , 3√ , …. Is

Answer 1

The complete question is:

The sum of 8 terms of G.P. 1 , √3 , 3 , 3√3 , …. is

Given:

The G.P. series 1 , √3 , 3 , 3√3 , ….

To find:

The sum of 8 terms of G.P. 1 , √ , 3 , 3√ , ….

Solution:

From the given information, we have the data as follows.

The G.P. series 1 , √3 , 3 , 3√3 , ….

The first term is, a₁ = 1

The ratio is,

r = a₂ / a₁

r = √3/1

r = √3

The given G.P. series represents the series containing 8 terms.

The sum of G.P. series is given by the formula as follows.

S = a [r^n - 1] / (r - 1)

Substitute the values in the above equation.

S = 1 [(√3)^8 - 1] / (√3 - 1)

Therefore, the sum of 8 terms of G.P. 1 , √3 , 3 , 3√3 , ….  is $S = \dfrac{(\sqrt{3})^8 - 1}{\sqrt3-1}$