Question

The 4th term of a G.P. is square of its second term, and the first term is − 3. Find its 7^th term.

Answer 1

$$\begin{gathered} \mathrm{Let}r\mathrm{be}\mathrm{the}\mathrm{common}\mathrm{ratio}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{G}.\mathrm{P}. \\ \mathrm{Then},a_4={\left(a_2\right)}^2\left[\mathrm{Given}\right] \\ \mathrm{Now},a{r}^3=a^2{r}^2 \\ \Rightarrow r=a\mathit{}\mathit{}\mathit{}\mathit{} \\ \Rightarrow r\mathit{}=-3\mathit{}\left[\mathrm{Putting}a\mathit{=}\mathit{-}\mathit{3}\right]\mathit{} \\ \therefore a_7=a{r}^6 \\ \Rightarrow a_7=\left(-3\right){\left(-3\right)}^6\left[\mathrm{Putting}a=-3\mathrm{and}r=-3\right] \\ \Rightarrow a_7=\left(-3\right)\left(-729\right) \\ \Rightarrow a_7=-2187 \\ \mathrm{Thus},\mathrm{the}{7}^{\mathrm{th}}\mathrm{term}\mathrm{of}\mathrm{the}\mathrm{G}.\mathrm{P}.\mathrm{is}-2187. \end{gathered}$$