Question Number 9324 by uchechukwu okorie favour last updated on 30/Nov/16
$${if}\:\:{x}=\frac{{a}\left(\mathrm{1}−{r}^{{n}} \right)}{\mathrm{1}−{r}}\:{make}\:{r}\:{the}\: \\ $$$${subject}\:{of}\:{the}\:{formula} \\ $$
Answered by mrW last updated on 30/Nov/16
$$\mathrm{let}\:\mathrm{k}=\frac{\mathrm{x}}{\mathrm{a}} \\ $$$$\mathrm{k}=\frac{\mathrm{1}−\mathrm{r}^{\mathrm{n}} }{\mathrm{1}−\mathrm{r}} \\ $$$$\mathrm{k}−\mathrm{kr}=\mathrm{1}−\mathrm{r}^{\mathrm{n}} \\ $$$$\mathrm{r}^{\mathrm{n}} −\mathrm{kr}+\left(\mathrm{k}−\mathrm{1}\right)=\mathrm{0} \\ $$$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{it}\:\mathrm{is}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{get} \\ $$$$\mathrm{a}\:\mathrm{formula}\:\mathrm{for}\:\mathrm{r}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{n}\:\mathrm{and}\:\mathrm{k}. \\ $$
Commented by uchechukwu okorie favour last updated on 30/Nov/16
$${hmmm} \\ $$