Tìm cấp số cộng ( un) có 5 số hạng, biết : { u1 +u5 = 7 { u3 + u4 = 9

Đáp án:

$\left\{\begin{array}{l} u_{n+1}=u_n+2\\u_{1}=\dfrac{-1}{2}\end{array} \right.$

Lời giải:

Ta có:

$\left\{\begin{array}{l} u_{n+1}=u_n+d\\u_{n+1}=u_1+nd\end{array} \right.$

$\Rightarrow \left\{\begin{array}{l} u_{1}+u_5=7\\u_{3}+u_4=9\end{array} \right.\Leftrightarrow \left\{\begin{array}{l} u_{1}+(u_1+4d)=7\\(u_{1}+2d)+(u_1+3d)=9\end{array} \right.$

$\Leftrightarrow \left\{\begin{array}{l} 2u_{1}+4d=7\\2u_{1}+5d=9\end{array} \right.\Leftrightarrow\left\{\begin{array}{l} d=2\\u_{1}=\dfrac{-1}{2}\end{array} \right.$

$\Leftrightarrow \left\{\begin{array}{l} u_{n+1}=u_n+2\\u_{1}=\dfrac{-1}{2}\end{array} \right.$