Question: Find an explicit formula for the geometric sequence below. \[ 2, \frac{2}{3}, \frac{2}{9},…

Find an explicit formula for the geometric sequence below.

\[ 2, \frac{2}{3}, \frac{2}{9}, \frac{2}{27}, \frac{2}{81} \]

Solution

Identify the first term of the sequence. \[ a_1 = 2 & \] Determine the common ratio \( r \). \[ r = \frac{\frac{2}{3}}{2} = \frac{1}{3} & \] Write the explicit formula for the geometric sequence. \[ a_n = 2 \left(\frac{1}{3}\right)^{n-1} & \]