Answer
The next three terms are $\frac{1}{6},0,$ and $-\frac{1}{6}$.
Work Step by Step
The given arithmetic sequence is
$\frac{5}{6},\frac{2}{3},\frac{1}{2},\frac{1}{3},...$
Each term is $\frac{1}{6}$ less than the previous term. so, the common difference is $\frac{1}{6}$.
The next three terms are
$\frac{1}{3}-\frac{1}{6}=\frac{1}{6}$
$\frac{1}{6}-\frac{1}{6}=0$
$0-\frac{1}{6}=-\frac{1}{6}$
Hence, the next three terms are $\frac{1}{6},0,$ and $-\frac{1}{6}$.
