$S_{15}=\dfrac{(u_1+u_{15}).15}{2}=375$
$\Leftrightarrow u_1+u_{15}=50$
$u_1^3+u_{15}^3=(u_1+u_{15})^3-3u_1^2u_{15}-3u_1u_{15}^2=97400$
$\Leftrightarrow (u_1+u_{15})^3-3u_1u_{15}(u_1+u_{15})=97400$
$\Leftrightarrow 50^3-50.3u_1.u_{15}=97400$
$\Leftrightarrow u_1.u_{15}=184$
$\Leftrightarrow u_1(50-u_1)=184$
$\Leftrightarrow u_1^2-50u_1+184=0$
$\Leftrightarrow u_1=4$ hoặc $u_1=46$
$+) u_1=4\Rightarrow u_{15}=46$
$u_{15}=u_1+14d$
$\Leftrightarrow d=3$
Vậy $u_n=4+(n-1).3$
$+) u_1=46\Rightarrow u_{15}=4$
$u_{15}=u_1+14d$
$\Leftrightarrow d=-3$
Vậy $u_n=46-3(n-1)$
