If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309 , then the sum of its first nine terms is :

Step-by-step solution

aligned & ar + ar ^3+ ar ^5=21, ar ^7+ ar ^9+ ar ¹¹=15309 & ar (1+ r ^2+ r ^4 )=21, ar ^7 (1+ r ^2+ r ^4 )=15309 aligned Eq ^ n ( 2) eq ^ n (1) (2) _ (1) ^ (2) . aligned & a r ^7 ar = 15309 21 r ^6=729 & a ( r ^9-1 ) r -1 = 7 91 (19683-1) 2 = 7 19682 91 2 & = 9841 13 =757 aligned