Find the common ratio of the geometric sequence. -8,2,-(1)/(2),ldots

To find the common ratio of a geometric sequence, we need to divide any term in the sequence by the previous term.<br /><br />Let's take the second term and divide it by the first term:<br />\[ r = \frac{2}{-8} = -\frac{1}{4} \]<br /><br />Now, let's verify this by checking the ratio between the third term and the second term:<br />\[ r = \frac{-\frac{1}{2}}{2} = -\frac{1}{4} \]<br /><br />Since the ratio is consistent between consecutive terms, the common ratio \( r \) of the geometric sequence is:<br />\[ r = -\frac{1}{4} \]