Answer
$a_{17} = 12,884,901,888$
Work Step by Step
Use the explicit formula to find a specific term in a geometric sequence:
$a_n = a_1 \bullet r^{n - 1}$
Let's find the common ratio:
$r = \frac{12}{3} = 4$
The common ratio $r$ is $4$. We are given that the first term of the series, $a_1$, is $3$. Substitute these values into the explicit formula to find the $17th$ term:
$a_{17} = 3 \bullet (4)^{17 - 1}$
Simplify the exponent:
$a_{17} = 3 \bullet (4)^{16}$
Evaluate the exponential term first:
$a_{17} = 3 \bullet 4,294,967,296$
Multiply to simplify:
$a_{17} = 12,884,901,888$
