Cho cấp số nhân (u_n) thỏa mãn \(\left\{ {\begin{array}{*{20}{c}}{{{\rm{u}}_{\rm{4}}} - {{\rm{u}}_{\rm{2}}}{\rm{ = 36}}}\\{{{\rm{u}}_{\rm{5}}} - {{\rm{u}}_{\rm{3}}}{\rm{ = 72}}}\end{array}} \right.\). Chọn khẳng định đúng?

\(\left\{ {\begin{array}{*{20}{c}}{{{\rm{u}}_{{\rm{20}}}}{\rm{ = 8}}{{\rm{u}}_{{\rm{17}}}}}\\{{{\rm{u}}_{\rm{1}}}{\rm{ + }}{{\rm{u}}_{\rm{5}}}{\rm{ = 272}}}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{c}}{{{\rm{u}}_{{\rm{20}}}}{\rm{ = }}{q^3}{{\rm{u}}_{{\rm{17}}}}}\\{{{\rm{u}}_{\rm{1}}}{\rm{ + }}{{\rm{u}}_{\rm{1}}}{\rm{.}}{{\rm{q}}^4}{\rm{ = 272}}}\end{array}} \right.\)

\( \Rightarrow \left\{ {\begin{array}{*{20}{c}}{{{\rm{q}}^{\rm{3}}}{\rm{ = 8}}}\\{{{\rm{u}}_{\rm{1}}}\left( {{\rm{1 + }}{{\rm{q}}^{\rm{4}}}} \right){\rm{ = 272}}}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{c}}{{\rm{q = 2}}}\\{{{\rm{u}}_{\rm{1}}}{\rm{ = 16}}}\end{array}} \right.\)

Đáp án cần chọn là: A

\(\left\{ {\begin{array}{*{20}{c}}{{u_1} = \frac{1}{2}}\\{{u_2} = 2{u_1}}\\{{u_3} = 2{u_2}}\\{...}\\{{u_n} = 2{u_{n - 1}}}\end{array}} \right.\)Nhân 2 vế ta được\[{{\rm{u}}_{\rm{1}}}{{\rm{u}}_{\rm{2}}}...{{\rm{u}}_{\rm{n}}}{\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}{\rm{.}}{{\rm{2}}^{{\rm{n}} - {\rm{1}}}}{\rm{.}}{{\rm{u}}_{\rm{1}}}{{\rm{u}}_{\rm{2}}}...{{\rm{u}}_{{\rm{n}} - {\rm{1}}}} \Leftrightarrow {{\rm{u}}_{\rm{n}}}{\rm{ = }}{{\rm{2}}^{{\rm{n}} - {\rm{2}}}}\]

Đáp án cần chọn là: B