Question

The product of the first five terms of a GP is 343.Find the third term of the GP.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{first}\mathrm{five}\mathrm{term}\mathrm{of}\mathrm{the}\mathrm{GP}\mathrm{are}\mathrm{a},\mathrm{ar},{\mathrm{ar}}^2,{\mathrm{ar}}^3\mathrm{and}{\mathrm{ar}}^4 \\ \mathrm{Now}\mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{their}\mathrm{product}\mathrm{is}343\mathrm{so}, \\ \mathrm{a}\times \mathrm{ar}\times {\mathrm{ar}}^2\times {\mathrm{ar}}^3\times {\mathrm{ar}}^4=343 \\ {\mathrm{a}}^5{\mathrm{r}}^{10}=343 \\ \mathrm{or}{\left({\mathrm{ar}}^2\right)}^5=343 \\ \mathrm{or}{\mathrm{ar}}^2={\left(343\right)}^{\frac{1}{5}} \\ \mathrm{and}{\mathrm{ar}}^2\mathrm{is}\mathrm{nothing}\mathrm{but}\mathrm{third}\mathrm{term}\mathrm{of}\mathrm{the}\mathrm{GP}. \\ \mathrm{So}\mathrm{third}\mathrm{term}\mathrm{of}\mathrm{the}\mathrm{GP}={\left(343\right)}^{\frac{1}{5}} \end{gathered}$$