The common difference is d = -4, since
-32 - (-28) = -4
-36 - (-32) = -4
-40 - (-36) = -4
and so on.
In the arithmetic sequence starting with [tex]a_1=-28[/tex] and common difference -4, the next term is obtained by adding -4 to the previous one:
[tex]a_1 =-28[/tex]
[tex]a_2 = a_1 + d = -28 - 4 = -32[/tex]
[tex]a_3 = a_2 + d = a_1+2d = -28-4\times2 = -36[/tex]
[tex]a_4 = a_3 + d = a_1+3d = -28-4\times3 = -40[/tex]
and so on, up the n-th term
[tex]a_n = a_{n-1}+d = a_1+(n-1)d = \boxed{-28-4(n-1)}[/tex]
