how do i find the pattern for:

Question

-4,8,-12,16

if the last number is negative, multiply by -1 then add 4
if the last number is positive, add 4, then multiply by -1

or how about

term_n+1 = (abs(term_n))*(-1)^n, where term₁ = -4, n>0

oops that last line should have said:
term_n+1 = (abs(term_n)+4)*(-1)^n, where term₁ = -4, n>0