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Câu hỏi: Cho cấp số nhân $\left( {{u}_{n}} \right)$ có công bội $q>0,{{u}_{2}}=4,{{u}_{4}}=9$, giá trị của ${{u}_{5}}$ bằng
A. $\dfrac{81}{4}$.
B. $\dfrac{-27}{2}$.
C. 6.
D. $\dfrac{27}{2}$.
A. $\dfrac{81}{4}$.
B. $\dfrac{-27}{2}$.
C. 6.
D. $\dfrac{27}{2}$.
Ta có: $\left\{ \begin{aligned}
& {{u}_{4}}={{u}_{1}}.{{q}^{3}} \\
& {{u}_{2}}={{u}_{1}}.q \\
\end{aligned} \right.\Rightarrow {{q}^{2}}=\dfrac{{{u}_{4}}}{{{u}_{1}}}=\dfrac{9}{4}\Rightarrow q=\dfrac{3}{2}$.
Suy ra ${{u}_{5}}={{u}_{4}}.q=\dfrac{27}{2}$.
& {{u}_{4}}={{u}_{1}}.{{q}^{3}} \\
& {{u}_{2}}={{u}_{1}}.q \\
\end{aligned} \right.\Rightarrow {{q}^{2}}=\dfrac{{{u}_{4}}}{{{u}_{1}}}=\dfrac{9}{4}\Rightarrow q=\dfrac{3}{2}$.
Suy ra ${{u}_{5}}={{u}_{4}}.q=\dfrac{27}{2}$.
Đáp án D.