Question

In a G.P.the first term is 7, the last term 448, and their sum is 889; find the common ratio.

Answer 1

$$\begin{gathered} \mathrm{Given}\mathrm{a}=7\mathrm{the}\mathrm{first}\mathrm{term}\mathrm{and} \\ \mathrm{We}\mathrm{know}\mathrm{that}{\mathrm{t}}_{\mathrm{n}}={\mathrm{ar}}^{\mathrm{n}-1}=7{\mathrm{r}}^{\mathrm{n}-1}=448 \\ 7{\mathrm{r}}^{\mathrm{n}}=448\mathrm{r} \\ \mathrm{Also}{\mathrm{S}}_{\mathrm{n}}=\frac{\mathrm{a}\left({\mathrm{r}}^{\mathrm{n}}-1\right)}{\mathrm{r}-1}=\frac{7\left({\mathrm{r}}^{\mathrm{n}}-1\right)}{\mathrm{r}-1}=\frac{7{\mathrm{r}}^{\mathrm{n}}-7}{\mathrm{r}-1} \\ 889=\frac{448\mathrm{r}-7}{\mathrm{r}-1} \\ 889\mathrm{r}-889=448\mathrm{r}-7 \\ \mathrm{Solving}\mathrm{we}\mathrm{get}\mathrm{r}=2. \end{gathered}$$