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Câu hỏi: Cho cấp số nhân $\left(u_n\right)$ thỏa mãn: $\left\{\begin{array}{l}u_1+u_3=10 \\ u_4+u_6=80\end{array}\right.$. Tìm $u_3$.
A. $u_3=4$.
B. $u_3=2$.
C. $u_3=8$.
D. $u_3=6$.
A. $u_3=4$.
B. $u_3=2$.
C. $u_3=8$.
D. $u_3=6$.
$\left\{\begin{array}{l}u_1+u_3=10 \\ u_4+u_6=80\end{array} \Leftrightarrow\left\{\begin{array}{l}u_1+u_1 q^2=10 \\ u_1 q^3+u_1 q^5=80\end{array} \Leftrightarrow\left\{\begin{array}{l}u_1\left(1+q^2\right)=10 \\ u_1 q^3\left(1+q^2\right)=80\end{array} \Leftrightarrow\left\{\begin{array}{l}u_1\left(1+q^2\right)=10 \\ q^3=8\end{array} \Leftrightarrow\left\{\begin{array}{l}u_1=2 \\ q=2\end{array}\right.\right.\right.\right.\right.$.
Vậy $u_3=8$.
Vậy $u_3=8$.
Đáp án C.
