$0, -4, -8, -12, \ldots$ are $APs$? If they form an $AP$,find the common difference $d$ and write three more terms.

(A) Given sequence: $0, -4, -8, -12, \ldots$
To check if the sequence is an $AP$,we calculate the difference between consecutive terms:
$a_{2} - a_{1} = (-4) - 0 = -4$
$a_{3} - a_{2} = (-8) - (-4) = -4$
$a_{4} - a_{3} = (-12) - (-8) = -4$
Since the difference $a_{k+1} - a_{k}$ is constant,the sequence is an $AP$ with common difference $d = -4$.
The next three terms are:
$a_{5} = a_{4} + d = -12 + (-4) = -16$
$a_{6} = a_{5} + d = -16 + (-4) = -20$
$a_{7} = a_{6} + d = -20 + (-4) = -24$
Thus,the common difference is $-4$ and the next three terms are $-16, -20, -24$.