Answer
The sequence is arithmetic.
Common difference $d=\frac{1}{3}$.
Work Step by Step
We compute the difference between each term and the preceding term. If the difference is same, then the sequence is arithmetic.
$a_{2}-a_{1}=-\frac{5}{3}-(-2)=\frac{1}{3}$
$a_{3}-a_{2}=-\frac{4}{3}-(-\frac{5}{3})=\frac{1}{3}$
$a_{4}-a_{3}=-1-(-\frac{4}{3})=\frac{1}{3}$
$a_{5}-a_{4}=-\frac{2}{3}-(-1)=\frac{1}{3}$
$a_{6}-a_{5}=-\frac{1}{3}-(-\frac{2}{3})=\frac{1}{3}$
The difference between each term and preceding term is constant and therefore the sequence is arithmetic.
Common difference $d=\frac{1}{3}$
