Question

Tìm số hạng đầu và công sai của các cấp số cộng sau, biết: \(\left\{{}\begin{matrix}2u_2-3u_4+4u_6=-20\\S_7=0\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}2u_2-3u_4+4u_6=-20\\S_7=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}2\left(u_1+d\right)-3\left(u_1+3d\right)+4\left(u_1+5d\right)=-20\\7\cdot\dfrac{\left[2u_1+6d\right]}{2}=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}2u_1+2d-3u_1-9d+4u_1+20d=-20\\u_1+3d=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}3u_1+13d=-20\\u_1+3d=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}3u_1+13d=-20\\3u_1+9d=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}22d=-20\\u_1=-3d\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}d=-\dfrac{10}{11}\\u_1=-3\cdot\dfrac{-10}{11}=\dfrac{30}{11}\end{matrix}\right.\)