Question

The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.

Answer 1

$$\begin{gathered} \mathrm{Let}a\mathrm{be}\mathrm{the}\mathrm{first}\mathrm{term}\mathrm{and}r\mathrm{be}\mathrm{the}\mathrm{common}\mathrm{ratio}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{G}.\mathrm{P}. \\ \therefore a_{4=}27\mathrm{and}{a}_7=729 \\ \Rightarrow a{r}^3=27\mathrm{and}a{r}^6=729 \\ \Rightarrow \frac{a{r}^6}{a{r}^3}=\frac{729}{27} \\ \Rightarrow r^3=3^3 \\ \Rightarrow r=3 \\ \mathrm{Putting}r=3\mathrm{in}a{r}^3=27 \\ a{\left(3\right)}^3=27 \\ \Rightarrow a=1 \\ \mathrm{Thus},\mathrm{the}\mathrm{given}\mathrm{G}.\mathrm{P}.\mathrm{is}1,3,9,... \end{gathered}$$