Answer
$a_{12}=10^{-8}$
Work Step by Step
We can find any term of the geometric sequence using the formula
$a_n=a_1r^{n-1}$.
Our geometric sequence is
$1000, 100, 10, \cdots$
So in our conditions:
$a_1=1000$
$r=\frac{a_2}{a_1}=\frac{100}{1000}=\frac{1}{10}.$
We have to find $a_{12}$:
$$a_{12}=a_1r^{11}=1000\cdot \dfrac{1}{10^{11}}=\dfrac{10^3}{10^{11}}=10^{-8}$$
