Question: Find an explicit formula for the geometric sequence below. \[ -1, -\frac{1}{2}, -\frac{1}{4},…

Find an explicit formula for the geometric sequence below.

\[ -1, -\frac{1}{2}, -\frac{1}{4}, -\frac{1}{8}, -\frac{1}{16} \]

Solution

Identify the first term of the sequence. \[ a_1 = -1 \] Determine the common ratio by dividing the second term by the first term. \[ r = \frac{-\frac{1}{2}}{-1} = \frac{1}{2} \] Write the explicit formula for the geometric sequence using the first term and the common ratio. \[ a_n = a_1 \cdot r^{n-1} = -1 \cdot \left(\frac{1}{2}\right)^{n-1} \]