The third sequence.
Step-by-step explanation:
In an arithmetic sequence, the difference between two consecutive terms is the same.
For each option, find the difference between consecutive terms:
First option:
![4 - 2 = 2](/tpl/images/0526/4490/91972.png)
.
![8 - 4 = 4](/tpl/images/0526/4490/8b721.png)
.
![16 - 8 = 8](/tpl/images/0526/4490/1d3e5.png)
.
The differences are not the same. As a result, this option is not an arithmetic sequence.
Second option:
![4 - 12 = -8](/tpl/images/0526/4490/2f2bc.png)
.
![\displaystyle \frac{4}{3} - 4 = -\frac{8}{3}](/tpl/images/0526/4490/44209.png)
.
![\displaystyle \frac{16}{3} - \frac{4}{3} = \frac{12}{3} = 4](/tpl/images/0526/4490/b5ef4.png)
.
The differences are not the same. As a result, this option is not an arithmetic sequence, either.
Third option:
![\displaystyle -\frac{1}{2} - \frac{1}{2} = -1](/tpl/images/0526/4490/eaee4.png)
.
![\displaystyle -\frac{3}{2} - \left(-\frac{1}{2}\right) = -\frac{3}{2} + \frac{1}{2} = -1](/tpl/images/0526/4490/d8baa.png)
.
![\displaystyle -\frac{5}{2} - \left(-\frac{3}{2}\right) = -\frac{5}{2} + \frac{3}{2} = -1](/tpl/images/0526/4490/638e5.png)
.
The differences are all
. As a result, this option is indeed an arithmetic sequence. Its common difference is
.
Fourth option:
![\displaystyle -\frac{1}{2} - \frac{1}{2} = -1](/tpl/images/0526/4490/eaee4.png)
.
![\displaystyle \frac{1}{2} - \left(-\frac{1}{2}\right) = \frac{1}{2} + \frac{1}{2} = 1](/tpl/images/0526/4490/9b004.png)
.
![\displaystyle -\frac{1}{2}\right - \frac{1}{2} = -1](/tpl/images/0526/4490/5a994.png)
.
The differences are varying between
and
. As a result, this option is not an arithmetic sequence.