Answer
The common ratio is $\frac{1}{12}$.
The fifth term is $\frac{1}{144}$ .
$a_{n} = 144(\frac{1}{12})^{n-1}$
Work Step by Step
The terms given are 144, -12, 1, -$\frac{1}{12}$
Since each term is multiplied by -$\frac{1}{12}$ to get to the next, the common ratio is -$\frac{1}{12}$. The fifth term = the fourth term $\times$ common ration = $-\frac{1}{12} \times -\frac{1}{12} = \frac{1}{144}$. The formula for the nth term of a geometric sequence is written in the form $a_{n} = a(r)^{n-1}$ since the first term (a) is 144 and the common ratio (r) is $-\frac{1}{12}$.
Plug these into the formula to get $a_{n} = 144(\frac{1}{12})^{n-1}$
