\[ \textbf{We see an ``multiply \& alternate add/subtract'' pattern in each sequence.} \] \[ \text{(1) } 8,\ 17,\ 33,\ 67,\ 133,\ ? \] Check: \[ 8\times2+1=17,\quad 17\times2-1=33,\quad 33\times2+1=67,\quad 67\times2-1=133. \] So the rule is ``\(\times2\) and alternate \(+1,-1\)''. Hence \[ 133\times2+1=267. \] \[ \boxed{(1)\;267} \] \bigskip \[ \text{(2) } 7,\ 23,\ 67,\ 203,\ 607,\ ? \] Check: \[ 7\times3+2=23,\quad 23\times3-2=67,\quad 67\times3+2=203,\quad 203\times3-2=607. \] Rule: ``\(\times3\) and alternate \(+2,-2\)''. Hence \[ 607\times3+2=1823. \] \[ \boxed{(2)\;1823} \] \bigskip \[ \text{(3) } 6,\ 27,\ 105,\ 423,\ 1689,\ ? \] Check: \[ 6\times4+3=27,\quad 27\times4-3=105,\quad 105\times4+3=423,\quad 423\times4-3=1689. \] Rule: ``\(\times4\) and alternate \(+3,-3\)''. Hence \[ 1689\times4+3=6759. \] \[ \boxed{(3)\;6759} \]