(i) ( 12, 16, 20, \ldots )

This is an arithmetic sequence with first term ( a = 12 ) and common difference ( d = 4 ).

Next four terms: [ \begin{align*} a_4 &= 20 + 4 = 24 \ a_5 &= 24 + 4 = 28 \ a_6 &= 28 + 4 = 32 \ a_7 &= 32 + 4 = 36 \end{align*} ]

Answer: ( 24, 28, 32, 36 )

(ii) ( 3, 1, -1, \ldots )

Common difference ( d = 1 - 3 = -2 ).

Next four terms: [ \begin{align*} a_4 &= -1 + (-2) = -3 \ a_5 &= -3 + (-2) = -5 \ a_6 &= -5 + (-2) = -7 \ a_7 &= -7 + (-2) = -9 \end{align*} ]

Answer: ( -3, -5, -7, -9 )