Question

Answer 1

Answer 2

\(S_5=\dfrac{5\left(2u_1+4d\right)}{2}=5\Rightarrow u_1+2d=1\)

\(\Rightarrow u_1=1-2d\)

\(u_1u_2u_3u_4u_5=5\)

\(\Rightarrow\left(1-2d\right)\left(1-d\right).1.\left(1+d\right)\left(1+2d\right)=45\)

\(\Rightarrow\left(1-d^2\right)\left(1-4d^2\right)=45\)

\(\Rightarrow4d^4-5d^2-44=0\Rightarrow\left[{}\begin{matrix}d^2=4\\d^2=-\dfrac{11}{4}< 0\left(loại\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}d=2\Rightarrow u_1=-3\\d=-2\Rightarrow u_1=5\end{matrix}\right.\)