Answer
$a_{20} = 824,633,720,832$
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 $20th$ term:
$a_{20} = 3 \bullet (4)^{20 - 1}$
Simplify the exponent:
$a_{20} = 3 \bullet (4)^{19}$
Evaluate the exponential term first:
$a_{20} = 3 \bullet 274,877,906,944$
Multiply to simplify:
$a_{20} = 824,633,720,832$
