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  • If arithmatic means  and three geometric means <img alt="(G.Ms)" src="http://entrancec

If m arithmatic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4^{th} A.M. is equal to 2^{nd} G.M., then m is equal to _______.
Option: 1 13
Option: 2 26
Option: 3 39
Option: 4 52

Answers (1)

best_answer

\\3, \mathrm{~A}_{1}, \mathrm{~A}_{2} \ldots \ldots . \mathrm{A}_{\mathrm{m}}, 24 3\\\\ \mathrm{~d}=\frac{243-3}{\mathrm{~m}+1}=\frac{240}{\mathrm{~m}+1} \\ \\\text { Now } 3, \mathrm{G}_{1}, \mathrm{G}_{2}, \mathrm{G}_{3}, 243

\begin{aligned} & \mathrm{r}=\left(\frac{243}{3}\right)^{\frac{1}{3+1}}=3 \\ \therefore \quad & \mathrm{A}_{4}=\mathrm{G}_{2} \\ \Rightarrow \quad & \mathrm{a}+4 \mathrm{~d}=\mathrm{ar}^{2} \\ & 3+4\left(\frac{240}{\mathrm{~m}+1}\right)=3(3)^{2} \\ & \mathrm{~m}=39 \end{aligned}

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himanshu.meshram

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