$P=u_2^2+u_3^2+u_4^2$
$=(u_1+d)^2+(u_1+2d)^2+(u_1+3d)^2$
$=3u_1^2+2u_1d+d^2+4u_1d+4d^2+6u_1d+9d^2$
Mà $d=-3$
$\to P=3u_1^2-36u_1+126$
$=3(u_1^2-12u_1+42)$
$=3(u_1-6)^2+18\ge 18$
$P_{\min}=18\Leftrightarrow u_1=6$
$u_{100}=u_1+99d=-291$
$\to S_{100}=\dfrac{(6-291).100}{2}=-14250$