math
posted by mike .
if an is a geometric sequence where a1=4 and the sum of an=12. how would you find the common ratio of the sequence? please help

You must mean the infinite sum of ALL an, up to infinity. Partial sums cannot all be the same.
Let the common ratio be x.
4(1 + x + x^2 + ...) = 12
(1 + x + x^2 + ...) = 3
Now, recognize that the infinite series adds up to 1/(1x).
1/(1x) = 3
1/x = 1/3
x = 2/3