Question

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

Answer 1

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/(1-x).
1/(1-x) = 3
1/x = 1/3
x = 2/3