[tex]\Large\boxed{\begin{array}{l}\sf S_6=12~a_6=7\\\\\sf S_6=\dfrac{\backslash\!\!\!6^3\cdot(a_1+7)}{\backslash\!\!\!2}\\\sf S_6=3a_1+21\\\sf 3a_1+21=12\\\sf 3a_1=12-21\\\sf 3a_1=-9\\\sf a_1=-\dfrac{9}{3}\\\\\sf a_1=-3\\\sf a_6=a_1+5r\\\sf 7=-3+5r\\\sf 5r=7+3\\\sf 5r=10\\\sf r=\dfrac{10}{5}\\\\\sf r=2\\\\\sf (-3,-1,1,3,5,7)\end{array}}[/tex]