We know that in arithmetic sequnce the common difference we can calculate

\(d=a_2-a_1=a_3-a_2=...a_n-a_{n-1}\)

To check if the given sequence is arithmetic, consider first difference. The following is true

\(d=a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4\)

\(-8=4-12=-4-4=-12+4=-20+12\)

Since the first difference is constant it implies that the given sequence is arithmetic.

\(d=a_2-a_1=a_3-a_2=...a_n-a_{n-1}\)

To check if the given sequence is arithmetic, consider first difference. The following is true

\(d=a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4\)

\(-8=4-12=-4-4=-12+4=-20+12\)

Since the first difference is constant it implies that the given sequence is arithmetic.