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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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{ar}+\mathrm{ar}^3+\mathrm{ar}^5=21, \quad \mathrm{ar}^7+\mathrm{ar}^9+\mathrm{ar}^{11}=15309 \quad \ldots (1) \ & \Rightarrow \operatorname{ar}\left(1+\mathrm{r}^2+\mathrm{r}^4ight)=21, \quad \operatorname{ar}^7\left(1+\mathrm{r}^2+\mathrm{r}^4ight)=15309 \quad \ldots (2) \end{aligned}$ $\begin{aligned} & \Rightarrow \frac{\mathrm{a} \cdot \mathrm{r}^7}{\mathrm{ar}}=\frac{15309}{21} \Rightarrow \mathrm{r}^6=729 \ & \Rightarrow \frac{\mathrm{a} \cdot\left(\mathrm{r}^9-1ight)}{\mathrm{r}-1}=\frac{\frac{7}{91}(19683-1)}{2}=\frac{7 	imes 19682}{91 	imes 2} \ & =\frac{9841}{13}=757\end{aligned}$ *

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…

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