What is the common ratio of the geometric series below?
24 plus left parenthesis negative 8 right parenthesis plus start fraction 8 over 3 end fraction plus left parenthesis negative start fraction 8 over 9 end fraction right parenthesis plus ellipsis
(1 point)
Responses
negative 3
Image with alt text: negative 3
negative one-third
Image with alt text: negative one-third
one-third
Image with alt text: one-third
3
To find the common ratio of a geometric series, we need to find the ratio between any two consecutive terms.
In this series, the terms are:
24, -8, 8/3, -8/9, ...
To find the ratio, we divide each term by the previous term:
-8/24 = -1/3
(8/3)/(-8) = -1/3
(-8/9)/(8/3) = -1/3
The ratio between any two consecutive terms is -1/3.
Therefore, the common ratio of the geometric series is -1/3.