In the first, the word "solve" implies an equals sign, I don't see one.
In the second, I am assuming n is a fixed number.
(1-r)S=a-ar^n
ar^n+rS=aS-a check that.
Now solutions to that depends on several things.
when n>=3, it has specific solution methods only for specific values. At n=2, the quadratic equation is very famous. At 1, any Algebra student should be able to handle it.
The PI symbol in the first bothers me you might be studying something very advance, normally reserved for upper college students. Look the PI symbol in Math, it is more than 3.14159...
http://en.wikipedia.org/wiki/Pi_%28letter%29
Solve for s
пr(s+r)
Solve for a
S= a(1-r^n)/1-r
2 answers
Since we're not solving for r, the polynomial stuff doesn't matter.
(1-r)S = a(1-r^n)
a = (1-r)S/(1-r^n)
(1-r)S = a(1-r^n)
a = (1-r)S/(1-r^n)