If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243 , then the sum of the first 50 terms of this G.P. is :

Step-by-step solution

Let a, ar, ar … 2 … . . be terms of G.P. Given, T 2 + T 3 + T 4 = 3    ⇒ ar 1 + r + r 2 = 3 T 6 + T 7 + T 8 = 243    ⇒ a r 5 1 + r + r 2 = 243 by (i) and (ii) r 4 = 81   ⇒ r = 3 ∴ a = 1 13 S 50 = a r 50 - 1 r - 1 = 3 50 - 1 26