The sequence is an arithmetic sequence because the difference between consecutive terms is -30.
We need to subtract a term from its consecutive number in the sequence, for example
Difference between second and first term
-51 - (-21) = -51 + 21 = -30
Difference between third and second term
-81 - ( -51) = -81 + 51 = -30
Difference between fourth and third term
-111 - (-81) = -111 + 81 = -30
And so on, If one realizes that the difference between consecutive terms is the same it would be an arithmetic sequence.