The first term of a geometric sequence is -2 and the common ratio is -(1)/(4) What are the next three terms of the sequence? -(1)/(2),-(1)/(8),-(1)/(32) (1)/(2),-(1)/(8),(1)/(32) -(1)/(2),(1)/(8),-(1)/(32) (1)/(2),(1)/(8),(1)/(32)

To find the next three terms of the geometric sequence, we can use the formula for the nth term of a geometric sequence: $a_n = a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term and $r$ is the common ratio.<br /><br />Given that the first term is $-2$ and the common ratio is $-\frac{1}{4}$, we can calculate the next three terms as follows:<br /><br />1. Second term: $a_2 = -2 \cdot \left(-\frac{1}{4}\right)^1 = -2 \cdot -\frac{1}{4} = \frac{1}{2}$<br /><br />2. Third term: $a_3 = -2 \cdot \left(-\frac{1}{4}\right)^2 = -2 \cdot \frac{1}{16} = -\frac{1}{8}$<br /><br />3. Fourth term: $a_4 = -2 \cdot \left(-\frac{1}{4}\right)^3 = -2 \cdot -\frac{1}{64} = \frac{1}{32}$<br /><br />Therefore, the next three terms of the sequence are $\frac{1}{2}, -\frac{1}{8}, \frac{1}{32}$.<br /><br />The correct answer is: $\frac{1}{2}, -\frac{1}{8}, \frac{1}{32}$.