Find the common ratio of the geometric sequence. 5,(10)/(3),(20)/(9),ldots Show your work here

To find the common ratio of the 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 /><br />$\frac{\frac{10}{3}}{5} = \frac{10}{3} \cdot \frac{1}{5} = \frac{10}{15} = \frac{2}{3}$<br /><br />Now let's take the third term and divide it by the second term:<br /><br />$\frac{\frac{20}{9}}{\frac{10}{3}} = \frac{20}{9} \cdot \frac{3}{10} = \frac{60}{90} = \frac{2}{3}$<br /><br />Since the common ratio is the same for both pairs of consecutive terms, we can conclude that the common ratio of the geometric sequence is $\frac{2}{3}$.