Решите пожалуйста 20 баллов

$1)\left \{ {{a_{9}-a_{4} =90 } \atop {a_{6}=55 }} \right.\\\\\left \{ {{a_{1}+8d-a_{1} -3d=90} \atop {a_{1}+5d=55 }} \right.\\\\\left \{ {{5d=90} \atop {a_{1}=55-5d }} \right.\\\\\left \{ {{d=18} \atop {a_{1}=55-5*18 }} \right. \\\\\left \{ {{d=18} \atop {a_{1} =-35}} \right.$

$S_{n}=\frac{2a_{1}+d(n-1) }{2}*n=\frac{2*105-7(n-1)}{2}*n=\frac{210-7n+7}{2}*n=\frac{217-7n}{2}*n\\\\ \frac{(217-7n)*n}{2}=0\\\\217n-n^{2}=0\\\\n(217-7n)=0\\\\n_{1}=0\\\\217-7n=0\\\\n_{2}=31$

n = 0 - не подходит

Ответ : 31