Answer
Yes it is an arithmetic sequence, and the common difference is -$\frac{1}{6}$
Work Step by Step
The difference between consecutive terms is constant in an arithmetic sequence.
The sequence: $\frac{1}{2}, \frac{1}{3}, \frac{1}{6}, 0$
Finding the pattern:
Difference between 1st and 2nd term:
2nd term-1st term=Difference
$\frac{1}{3}-\frac{1}{2} $= -$\frac{1}{6}$
Difference between 2nd and 3rd term:
3rd term-2nd term=Difference
$\frac{1}{6}-\frac{1}{3}$= -$\frac{1}{6}$
Difference between 3rd and 4th term:
4th term-3rd term=Difference
0-$\frac{1}{6}$= -$\frac{1}{6}$
The common difference is -$\frac{1}{6}$ and it is constant thus this is an arithmetic sequence.
