Answer
$a_n = 2^{n - 1}$
Work Step by Step
The explicit formula of a geometric sequence is given by:
$a_n = a_1 \cdot r^{n - 1}$
Let's find the common ratio:
$r = \frac{2}{1} = 2$
The common ratio $r$ is $2$. We are given that the first term of the series, $a_1$, is $1$. Substitute these values into the explicit formula:
$a_n = 1 \cdot 2^{n - 1}$
Simplify:
$a_n = 2^{n - 1}$
