Let $a_{1},a_{2},a_{3},\ldots$. be a G.P. of increasing positive terms such that $a_{2} \cdot a_{3}

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Let $a_{1},a_{2},a_{3},\ldots$. be a G.P. of increasing positive terms such that $a_{2} \cdot a_{3} \cdot a_{4} = 64$ and $a_{1} + a_{3} + a_{5} = \frac{813}{7}$. Then $a_{3} + a_{5} + a_{7}$ is equal to :

Accepted Answer

ar $.{ar}^{2}.{ar}^{3} = 64$$${a^{3}r^{6} = 64\ \Rightarrow {ar}^{2} = 4 }{a + {ar}^{2} + {ar}^{4} = \frac{813}{7} }{r^{2} = 28 }$$${ar}^{2} + {ar}^{4} + {ar}^{6} =$ ?$${ar}^{2}\left( 1 + r^{2} + r^{4} \right) = 4(1 + 28 + 784) = 3252$$

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