Google
Câu hỏi: Cho cấp số nhân $\left( {{u}_{n}} \right)$ có ${{u}_{2}}=-6$, ${{u}_{5}}=48$. Tính ${{S}_{5}}$.
A. $33$.
B. $-31$.
C. $93$.
D. $11$.
& {{u}_{1}}.q=-6 \\
& {{u}_{1}}.{{q}^{4}}=48 \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& {{u}_{1}}.q=-6 \\
& {{q}^{3}}=-8 \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& {{u}_{1}}=3 \\
& q=-2 \\
\end{aligned} \right.$.
Vậy ${{S}_{5}}=\dfrac{3\left( 1-{{(-2)}^{5}} \right)}{1-\left( -2 \right)}=33$.
A. $33$.
B. $-31$.
C. $93$.
D. $11$.
Ta có $\left\{ \begin{aligned}& {{u}_{1}}.q=-6 \\
& {{u}_{1}}.{{q}^{4}}=48 \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& {{u}_{1}}.q=-6 \\
& {{q}^{3}}=-8 \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& {{u}_{1}}=3 \\
& q=-2 \\
\end{aligned} \right.$.
Vậy ${{S}_{5}}=\dfrac{3\left( 1-{{(-2)}^{5}} \right)}{1-\left( -2 \right)}=33$.
Đáp án A.