Answer
$a_7=81$
Work Step by Step
We have to find $7$th term of the geometric sequence:
$\frac{1}{9}, -\frac{1}{3}, 1, 3, . . . $
$$a_n=a_1r^{n-1}$$
$$n=7, \quad a_1=\dfrac{1}{9}, \quad r=\frac{-\frac{1}{3}}{\frac{1}{9}}=-3$$
$$a_7=\dfrac{1}{9}(-3)^{7-1}$$
$$a_7=\dfrac{(-3)^6}{9}=\dfrac{(-3)^6}{3^2}=\dfrac{(-1)^63^6}{3^2}$$
$$a_7=3^4=81$$