#s = (a(r^n -1))/(r-1)# Making #'r'# the subject formula..?
1 Answer
This is not generally possible...
Explanation:
Given:
#s = (a(r^n-1))/(r-1)#
Ideally we want to derive a formula like:
#r = "some expression in " s, n, a#
This is not going to be possible for all values of
#s = (a(r^color(blue)(1)-1))/(r-1) = a#
Then
Also, note that if
Let us see how far we can get in general:
First multiply both sides of the given equation by
#s(r-1) = a(r^n-1)#
Multiplying out both sides, this becomes:
#sr-s=ar^n-a#
Then subtracting the left hand side from both sides, we get:
#0 = ar^n-sr+(s-a)#
Assuming
#r^n-s/a r+(s/a-1) = 0#
Note that for any values of
Let us attempt to factor out
#0 = r^n-s/a r+(s/a-1)#
#color(white)(0) = r^n-1-s/a(r-1)#
#color(white)(0) = (r-1)(r^(n-1)+r^(n-2)+...+1-s/a)#
So dividing by
#r^(n-1)+r^(n-2)+...+1-s/a = 0#
The solutions of this will take very different forms for different values of