Select all sequences that are geometric. (A) 1.5,6,24,96,ldots x (B) 2,4,6,8,10,ldots 25,5,1,(1)/(5),(1)/(25),ldots x (D) The circumference of a tree trunk grows 2.5 inches each year: 8.25,10.75,13.25,15.75,ldots (E) 1,-1.5,2.25,-3.375,ldots COMPLETE For each of the geometric sequences, determine the common ratio. Sequence A has common ratio 14 square COMPLETE Sequence C has common ratio square COMPLETE Sequence E has common ratio square square

To determine if a sequence is geometric, we need to check if the ratio between consecutive terms is constant. Let's analyze each sequence:<br /><br />(A) $1.5, 6, 24, 96, \ldots$<br />To find the common ratio, divide each term by the previous term:<br />$\frac{6}{1.5} = 4$, $\frac{24}{6} = 4$, $\frac{96}{24} = 4$<br />The common ratio is 4, so this sequence is geometric.<br /><br />(B) $2, 4, 6, 8, 10, \ldots$<br />Divide each term by the previous term:<br />$\frac{4}{2} = 2$, $\frac{6}{4} = 1.5$, $\frac{8}{6} \approx 1.33$, $\frac{10}{8} = 1.25$<br />The ratios are not constant, so this sequence is not geometric.<br /><br />(C) $25, 5, 1, \frac{1}{5}, \frac{1}{25}, \ldots$<br />Divide each term by the previous term:<br />$\frac{5}{25} = \frac{1}{5}$, $\frac{1}{5} = \frac{1}{5}$, $\frac{\frac{1}{5}}{1} = \frac{1}{5}$, $\frac{\frac{1}{25}}{\frac{1}{5}} = \frac{1}{5}$<br />The common ratio is $\frac{1}{5}$, so this sequence is geometric.<br /><br />(D) The circumference of a tree trunk grows 2.5 inches each year:<br />$8.25, 10.75, 13.25, 15.75, \ldots$<br />Divide each term by the previous term:<br />$\frac{10.75}{8.25} \approx 1.3$, $\frac{13.25}{10.75} \approx 1.24$, $\frac{15.75}{13.25} \approx 1.19$<br />The ratios are not constant, so this sequence is not geometric.<br /><br />(E) $1, -1.5, 2.25, -3.375, \ldots$<br />Divide each term by the previous term:<br />$\frac{-1.5}{1} = -1.5$, $\frac{2.25}{-1.5} = -1.5$, $\frac{-3.375}{2.25} = -1.5$<br />The common ratio is -1.5, so this sequence is geometric.<br /><br />Now, let's determine the common ratios for the geometric sequences:<br /><br />Sequence A has a common ratio of 4.<br /><br />Sequence C has a common ratio of $\frac{1}{5}$.<br /><br />Sequence E has a common ratio of -1.5.