Question

In a geometric progression , the second term is −4 and the sum to infinity is 9 .Find the common ratio.

I did all the working out to get to (3r-4)(3r+1)

i know the answer is -1/3 but i dont understand why? since -1/3 makes sum of infinity 9.000000023
and 4/3 gives 9
please explain why the answer is -1/3

Answer 1

For a geomertic sequence to converge the ratio must by less than 1.
The sum is (a1 - a1*r^n) / (1 - r).
So if 'r' is > 1 then the value of 'a1*r^n' will keep increasing and you will get an infinit large or small sum. On the other hand, if r < 0 then r^n will eventually become 0, and the sum of the sequence is then given by a1/(1-r)

Answer 2

Actually r should be -1 < r < 1 for a geometric sequence to converge.

Answer 3

thank you very much, i did not know about the -1 < r < 1
i kinda missed the topic... thank you, you are a hero!