Answer
$a_7 = 729$
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:
$r = \frac{-3}{1} = -3$
The common ratio $r$ is $-3$. We are given that the first term of the series, $a_1$, is $1$. Substitute these values into the explicit formula to find the $7th$ term:
$a_7 = 1 \bullet (-3)^{7 - 1}$
Simplify the exponent:
$a_7 = 1 \bullet (-3)^{6}$
Evaluate the exponential term first:
$a_7 = 1 \bullet 729$
Multiply to simplify:
$a_7 = 729$
