Answer
The sixth term is -648
Work Step by Step
1. Find the common ratio. The 2nd term ($-\frac{1}{2}$) is the first term ($\frac{1}{12}$) multiplied by -6 so the common ratio, r, = -6.
2. Find the first term: The first term is given as $\frac{1}{12}$. The first term = a.
3. Create a formula for the geometric sequence in the form $a_{n} = a(r)^{n-1}$ : $a_n = \frac{1}{12}(-6)^{n-1}$
4. Plug in n = 6 to get the sixth term: $a_n = \frac{1}{12}(-6)^{6-1}$ $a_n = \frac{1}{12}(-6)^{5}$ = -648.
