An arithmetic sequence is effectively just a list of numbers that have a definite, predictable pattern. In the above problem, one might notice that if you start on the far left number -13, and add 7, you get -6, which is the next number in the series. If you add 7 again, you get 1, the NEXT number, and lastly, if you add 7 one more time, you get 8.
In sum, yes, the above is an arithmetic sequence. More specifically, it's an arithmetic sequence governed by the rule of adding 7 as you progress from left to right.