Answer
$a_{10} = 2560$
Work Step by Step
Use the explicit formula to find a specific term in a geometric sequence:
$a_n = a_1 \cdot r^{n - 1}$
Let's find the common ratio:
$r = \frac{10}{5} = 2$
The common ratio $r$ is $2$. We are given that the first term of the series, $a_1$, is $5$. Substitute these values into the explicit formula to find the $10th$ term:
$a_{10} = 5 \cdot (2)^{10 - 1}$
Simplify the exponent:
$a_{10} = 5 \cdot (2)^{9}$
Evaluate the exponential term first:
$a_{10} = 5 \cdot 512$
Multiply to simplify:
$a_{10} = 2560$
