Cho cấp số nhân $\Large (u_n)$ thỏa mãn: $\Large \left\{\begin{align}

Cho cấp số nhân $\Large (u_n)$ thỏa mãn: $\Large \left\{\begin{align} & u_4=\dfrac{2}{27} \\ & u_3=242u_8 \end{align}\right.$. Viết 5 số hạng đầu của cấp số

• A.

  $\Large u_1=2$; $\Large u_2=\dfrac{2}{5}$; $\Large u_3=\dfrac{2}{9}$; $\Large u_4=\dfrac{2}{27}$; $\Large u_5=\dfrac{2}{81}$.

• B.

  $\Large u_1=2$; $\Large u_2=\dfrac{2}{3}$; $\Large u_3=\dfrac{2}{9}$; $\Large u_4=\dfrac{2}{27}$; $\Large u_5=\dfrac{2}{64}$.

• C.

  $\Large u_1=1$; $\Large u_2=\dfrac{2}{3}$; $\Large u_3=\dfrac{2}{9}$; $\Large u_4=\dfrac{2}{27}$; $\Large u_5=\dfrac{2}{81}$.

• D.

  $\Large u_1=2$; $\Large u_2=\dfrac{2}{3}$; $\Large u_3=\dfrac{2}{9}$; $\Large u_4=\dfrac{2}{27}$; $\Large u_5=\dfrac{2}{81}$.

Ta có:

$\Large \left\{\begin{align} & u_4=\dfrac{2}{27} \\ & u_3=243u_8 \end{align}\right.$ $\Large \Leftrightarrow \left\{\begin{align} & u_1.q^3=\dfrac{2}{27} \\ & u_1.q^2=243u_1.q^7 \end{align}\right.$

$\Large \Leftrightarrow \left\{\begin{align} & u_1=\dfrac{2}{27.q^3} \\ & \dfrac{1}{q^5}=243 \end{align}\right.$ $\Large \Leftrightarrow \left\{\begin{align} & u_1=2 \\ & q=\dfrac{1}{3} \end{align}\right.$ $\Large \Leftrightarrow u_n=2.\left(\dfrac{1}{3}\right)^{n-1}$

$\Large u_2=\dfrac{2}{3^1}=\dfrac{2}{3}$;

$\Large u_3=\dfrac{2}{3^2}=\dfrac{2}{9}$;

$\Large u_4=\dfrac{2}{3^3}=\dfrac{2}{27}$;

$\Large u_5=\dfrac{2}{3^4}=\dfrac{2}{81}$.

Chọn D.