how do i find the pattern for:

-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

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

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

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