[tex]\displaystyle\bf\\S_{n} =6n-n^{2} \\\\a_{1} =S_{1}=6\cdot 1-1^{2} =6-1=5\\\\S_{7} =6\cdot 7-7^{2}=42-49=-7\\\\\\S_{7} =\frac{a_{1} + a_{7} }{2}\cdot 7\\\\\\2S_{7} =(a_{1} + a_{7} )\cdot 7\\\\\\2\cdot(-7)=(5+a_{7})\cdot 7\\\\\\-2=5+a_{7} \\\\\\\boxed{a_{7} =-7}[/tex]
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[tex]\displaystyle\bf\\S_{n} =6n-n^{2} \\\\a_{1} =S_{1}=6\cdot 1-1^{2} =6-1=5\\\\S_{7} =6\cdot 7-7^{2}=42-49=-7\\\\\\S_{7} =\frac{a_{1} + a_{7} }{2}\cdot 7\\\\\\2S_{7} =(a_{1} + a_{7} )\cdot 7\\\\\\2\cdot(-7)=(5+a_{7})\cdot 7\\\\\\-2=5+a_{7} \\\\\\\boxed{a_{7} =-7}[/tex]