\(\Rightarrow\left\{{}\begin{matrix}S_4=40\\S_8=3280\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\frac{u_1\left(q^4-1\right)}{q-1}=40\\\frac{u_1\left(q^8-1\right)}{q-1}=3280\end{matrix}\right.\)
Chia dưới cho trên ta được:
\(\frac{q^8-1}{q^4-1}=82\Leftrightarrow q^4+1=82\Rightarrow q^4=81\Rightarrow q=\pm3\)
- Với \(q=3\Rightarrow u_1=\frac{40\left(q-1\right)}{q^4-1}=1\)
\(\Rightarrow S_5=\frac{u_1\left(q^5-1\right)}{q-1}=121\)
- Với \(q=-3\Rightarrow u_1=\frac{40\left(q-1\right)}{q^4-1}=-2\)
\(\Rightarrow S_5=-122\)
