Question

find the sum of first 10 terms of the G.P 1,√3,3,3√3.......​

Answer 1

Step-by-step explanation:

Given---> 1 , √3 , 3 , 3√3, ......................

To find ----> Sum of first 10 terms

Solution---> ATQ, given GP is,

1 , √3 , 3 , 3√3 , ........................

First term = 1

Common ratio = second term / first term

= √3 / 1

= √3

So , a = 1 , r = √3 , n = 10 , Sₙ = ?

Sₙ = a ( 1 - rⁿ ) / ( 1 - r )

Sₙ = 1 { 1 - ( √3 )¹⁰ } / ( 1 - √3 )

= 1 - ( 3⁵ ) / ( 1 - √3 )

= 1 - 243 / ( 1 - √3 )

= -242 / - ( √3 - 1 )

= 242 / ( √ 3 - 1 )

Multiplying by conjugate of denominator , we get

= 242 ( √3 + 1 ) / ( √3 - 1 ) ( √3 + 1 )

= 242 ( √3 + 1 ) / ( √3 )² - ( 1 )²

= 242 ( √3 + 1 ) / ( 3 - 1 )

= 242 ( √3 + 1 ) / 2

= 121 ( √3 + 1 )