Question Number 69314 by mezihloic last updated on 22/Sep/19
$${if}\:\mathrm{5}\:{x}\:{y}\:\mathrm{40}\:{are}\:{in}\:{GP}\:.{find}\:{x}\:{and}\:{y} \\ $$
Commented by Rasheed.Sindhi last updated on 22/Sep/19
$$\frac{{x}}{\mathrm{5}}=\frac{{y}}{{x}}=\frac{\mathrm{40}}{{y}} \\ $$$${xy}=\mathrm{200} \\ $$$${x}^{\mathrm{2}} =\mathrm{5}{y}\Rightarrow{x}^{\mathrm{2}} =\mathrm{5}\left(\frac{\mathrm{200}}{{x}}\right)\Rightarrow{x}^{\mathrm{3}} =\mathrm{1000}\Rightarrow{x}=\mathrm{10} \\ $$$${y}=\frac{\mathrm{200}}{{x}}=\frac{\mathrm{200}}{\mathrm{10}}=\mathrm{20} \\ $$$${x}=\mathrm{10},\:{y}=\mathrm{20} \\ $$
Answered by Rasheed.Sindhi last updated on 22/Sep/19
$${t}_{{n}} ={ar}^{{n}−\mathrm{1}} \Rightarrow{t}_{\mathrm{4}} =\mathrm{5}{r}^{\mathrm{3}} =\mathrm{40}\Rightarrow{r}=\mathrm{2} \\ $$$${x}=\mathrm{5}{r}=\mathrm{5}\left(\mathrm{2}\right)=\mathrm{10}\: \\ $$$${y}=\mathrm{10}{r}=\mathrm{10}\left(\mathrm{2}\right)=\mathrm{20} \\ $$