The product of first four terms of a G.P. is $\frac{1}{1024}$. Then the product of second and third

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The product of first four terms of a G.P. is $\frac{1}{1024}$. Then the product of second and third terms is,\

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(d) : Let $a, a r, a r^{2}, a r^{3}$ be the first four terms of the G.P., then\ $(a r)\left(a r^{2}ight)\left(a r^{3}ight)=\frac{1}{1024}$\ $\Rightarrow \quad a^{4} r^{6}=\frac{1}{1024} \quad \Rightarrow\left(a^{2} r^{3}ight)^{2}=\left(\frac{1}{32}ight)^{2}$\ $\Rightarrow \quad a^{2} r^{3}=\frac{1}{32}$\ ∴ Product of second and third terms $=(a r)\left(a r^{2}ight)=a^{2} r^{3}=\frac{1}{32}$\