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 :

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​ 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 ​ Eq n ( 2 ) ​ ÷ eq n ( 1 ) (2) ( 1 ) ( 2 ) ​ ​ ⇒ ar a ⋅ r 7 ​ = 21 15309 ​ ⇒ r 6 = 729 ⇒ r − 1 a ⋅ ( r 9 − 1 ) ​ = 2 91 7 ​ ( 19683 − 1 ) ​ = 91 × 2 7 × 19682 ​ = 13 9841 ​ = 757 ​

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