a: \(\left\{{}\begin{matrix}u_1+u_5=51\\u_2+u_6=102\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}u_1\cdot\left(1+q^4\right)=51\\u_1\cdot q+u_1\cdot q^5=102\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}u_1\left(1+q^4\right)=51\\u_1\cdot q\cdot\left(1+q^4\right)=102\end{matrix}\right.\)
=>\(u_1\cdot q\cdot\dfrac{\left(q^4+1\right)}{u_1\left(q^4+1\right)}=\dfrac{102}{51}=2\)
=>q=2
\(u_1=\dfrac{51}{2^4+1}=\dfrac{51}{17}=3\)
=>Đúng
b: \(u_4=u_1\cdot q^3=3\cdot2^3=3\cdot8=24\)
=>Sai
c: \(u_{12}=u_1\cdot q^{11}=3\cdot2^{11}=6144\)
=>Sai
d: \(S_8=\dfrac{u_1\left(1-q^8\right)}{1-q}=\dfrac{3\cdot\left(1-2^8\right)}{1-2}=\dfrac{3\cdot\left(2^8-1\right)}{2-1}=3\left(2^8-1\right)=765\)
=>Đúng
