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[tex]\blue{\boxed{\begin{array}{l}\sf S_{13}=\dfrac{ 13\cdot(a_{13}+a_1)}{2}\\\sf 1183=\dfrac{13\cdot(169+a_1)}{2}\\\sf 13a_1+2197=2\cdot 1183\\\sf 13a_1=2366-2197\\\sf 13a_1=169\\\sf a_1=\dfrac{169}{13}\\\sf a_1=13\\\sf a_{13}=a_1+12r\\\sf 169=13+12r\\\sf 12r=169-13\\\sf 12r=156\\\sf r=\dfrac{156}{12}\\\sf r=13\end{array}}}[/tex]
