Asked 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
Answers
Answered by
drwls
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
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