if S_n =((a(r^n −1))/(r−1)) make r the subject of formula


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Question Number 28739 by NECx last updated on 29/Jan/18

$i f S_{n} = \frac{a (r^{n} - 1)}{r - 1}$ $m a k e r t h e s u b j e c t o f f o r m u l a$
	Answered by ajfour last updated on 30/Jan/18

	$T_{n} = {a r}^{n - 1}$ $\ln (\frac{T_{n}}{a}) = (n - 1) \ln r$ $\ln r = \frac{1}{n - 1} \ln (\frac{S_{n} - S_{n - 1}}{a})$ $r = e^{\frac{1}{n - 1} \ln (\frac{S_{n} - S_{n - 1}}{a})}$ $o r r = {(\frac{S_{n} - S_{n - 1}}{a})}^{\frac{1}{n - 1}} .$
	Commented by NECx last updated on 30/Jan/18

	$s t i l l h a v i n g a d o u b t h e r e . D o e s i t$ $m e a n t h e a c t u a l v a l u e s c a n n o t$ $b e i m p u t e d . I f i t i s d o n e t h e n r$ $c o m e s b a c k t o t h e e q u a t i o n .$
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