Cho cấp số cộng (un) thoả mãn

D

- Hướng dẫn giải

\(\left\{ \begin{array}{l}{u_5} + 3{u_3} - {u_2} = - 21\\3{u_7} - 2{u_4} = - 34\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}{u_1} + 4d + 3\left( {{u_1} + 2d} \right) - {u_1} - d = - 21\\3\left( {{u_1} + 6d} \right) - 2\left( {{u_1} + 3d} \right) = - 34\end{array} \right.\)

\( \Leftrightarrow \left\{ \begin{array}{l}3{u_1} + 9d = - 21\\{u_1} + 12d = - 34\end{array} \right. \\\Leftrightarrow \left\{ \begin{array}{l}{u_1} = 2\\d = - 3\end{array} \right. \\\Rightarrow {S_{15}} = \frac{{{u_1} + {u_{15}}}}{2}.15 = \frac{{{u_1} + {u_1} + 14d}}{2}.15 = - 285\)