Verified answer

[tex]\displaystyle\bf\\S_{n} =3n^{2} +7n\\\\S_{1} =a_{1}=3\cdot 1^{2} +7\cdot 1=3+7=10\\\\\boxed{a_{1}=10}\\\\S_{2} =3\cdot 2^{2} +7\cdot 2=3\cdot 4+14=12+14=26\\\\S_{2}=a_{1} + a_{2} \\\\a_{2} = S_{2} - a_{1} =26-10=16\\\\a_{2} =a_{1} +d\\\\d=a_{2} - a_{1} =16-10=6\\\\\boxed{d=6}[/tex]