[tex]\displaystyle\bf\\a_{1} =-4\\\\d=2\\\\S_{n} =84\\\\n=? \ , \ n > 0\\\\\\S_{n} =\frac{2a_{1} +d\cdot(n-1)}{2} \cdot n\\\\\\84=\frac{2\cdot(-4)+2\cdot(n-1)}{2} \cdot n\\\\\\84=\Big[-4+(n-1)\Big]\cdot n\\\\\\84=(-4+n-1)\cdot n\\\\\\84=(n-5)\cdot n\\\\\\n^{2} -5n-84=0\\\\D=(-5)^{2} -4\cdot (-84)=25+336=361=19^{2} \\\\\\n_{1} =\frac{5+19}{2} =12\\\\\\n_{2}=\frac{5-19}{2} =-7 < 0-neyd\\\\Otvet \ : \ 12[/tex]