Question Number 9323 by uchechukwu okorie favour last updated on 30/Nov/16
$${if}\:\:{x}=\frac{{a}\left(\mathrm{1}−{r}^{{n}} \right)}{\mathrm{1}−{r}}\:{make}\:{r}\:{the}\: \\ $$$${subject}\:{of}\:{the}\:{formula} \\ $$
Commented by geovane10math last updated on 30/Nov/16
![x = ((a(−r^n + 1))/(−r + 1)) = ((a[−(r^n − 1)])/(−(r − 1))) x = ((−a(r^n − 1))/(−(r − 1))) = ((a(r^n − 1))/(r − 1)) x is the sum of terms of a Geometric Progression ratio = r first term = a](https://www.tinkutara.com/question/Q9341.png)
$${x}\:=\:\frac{{a}\left(−{r}^{{n}} \:+\:\mathrm{1}\right)}{−{r}\:+\:\mathrm{1}}\:=\:\frac{{a}\left[−\left({r}^{{n}} \:−\:\mathrm{1}\right)\right]}{−\left({r}\:−\:\mathrm{1}\right)} \\ $$$${x}\:=\:\frac{−{a}\left({r}^{{n}} \:−\:\mathrm{1}\right)}{−\left({r}\:−\:\mathrm{1}\right)}\:=\:\frac{{a}\left({r}^{{n}} \:−\:\mathrm{1}\right)}{{r}\:−\:\mathrm{1}} \\ $$$$\boldsymbol{{x}}\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{sum}}\:\boldsymbol{{of}}\:\boldsymbol{{terms}}\:\boldsymbol{{of}}\:\boldsymbol{{a}}\:\boldsymbol{{Geometric}} \\ $$$$\boldsymbol{{Progression}} \\ $$$$\boldsymbol{{ratio}}\:=\:\boldsymbol{{r}} \\ $$$$\boldsymbol{{first}}\:\boldsymbol{{term}}\:=\:\boldsymbol{{a}} \\ $$$$ \\ $$