Cho cấp số nhân như sau \(({u_n})\)thỏa mãn: \(\left\{ {\begin{array}{*{20}{c}}{{u_4} = \dfrac{2}{{27}}}\\{{u_3} = 243{u_8}}\end{array}} \right.\).

* Hướng dẫn giải

 Ta có

\(\begin{array}{l}\left\{ {\begin{array}{*{20}{c}}{{u_4} = \dfrac{2}{{27}}}\\{{u_3} = 243{u_8}}\end{array}} \right. \Leftrightarrow \left\{ \begin{array}{l}{u_1}.{q^3} = \dfrac{2}{{27}}\\{u_1}.{q^2} = 243{u_1}.{q^7}\end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l}{u_1} = \dfrac{2}{{27.{q^3}}}\\\dfrac{1}{{{q^5}}} = 243\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}{u_1} = 2\\q = \dfrac{1}{3}\end{array} \right. \Leftrightarrow {u_n} = 2.{\left( {\dfrac{1}{3}} \right)^{n - 1}}\end{array}\)

\({u_2} = \dfrac{2}{{{3^1}}} = \dfrac{2}{3}\);

\({u_3} = \dfrac{2}{{{3^2}}} = \dfrac{2}{9}\);

\({u_4} = \dfrac{2}{{{3^3}}} = \dfrac{2}{{27}}\);

\({u_5} = \dfrac{2}{{{3^4}}} = \dfrac{2}{{81}}\).

Chọn D.