\({u_4} = {u_1} + 3d \Rightarrow 5 = - 1 + 3d \Leftrightarrow d = 2\)
a)
\(\begin{array}{l}{u_{10}} = {u_1} + 9d = - 1 + 9.2 = 17\\{S_{10}} = \dfrac{{10\left( {{u_1} + {u_{10}}} \right)}}{2} = \dfrac{{10.\left( { - 1 + 17} \right)}}{2} = 80\end{array}\)
b) \({u_n} = 197 \Leftrightarrow 197 = - 1 + \left( {n - 1} \right).2 \Leftrightarrow n = 100\)
c) \({S_n} = 85 \Leftrightarrow \dfrac{{n\left( {2.\left( { - 1} \right) + \left( {n - 1} \right).2} \right)}}{2} = 85\) \( \Leftrightarrow - 2n + 2n\left( {n - 1} \right) = 170\)
\( \Leftrightarrow 2{n^2} - 4n - 170 = 0 \Leftrightarrow \left[ \begin{array}{l}n = 1 + \sqrt {86} \\n = 1 - \sqrt {86} \end{array} \right.\left( {loai} \right)\)
Vậy không có n thỏa mãn.
