Find the sum of indicated terms of each of the following geometric progressions :
(i) 2, 4, 8, 16 ,…, 20 terms
(ii) ` 1 , (-2)/(3) , (4)/(9) , (-8)/(27) ,…, 10 ` terms

Explanation

(i) ` a = 2 , r = 2 `
` therefore S_(20) = (a(r^(20) -1))/( r -1)`
` = ( 2xx(2^(20) -1))/(2-1) = 2 (2^(10) -1)`
` (ii) a = 1 , r = (-2)/(3)`
` therefore S_(10) = (a (1 - r^(10)))/(1-r) = (1 - ((-2)/(3))^(10))/( 1 + (2)/(3))`
` = (3)/(5) [ 1 - ((2)/(3))^(10)]` .