Ответ: S₉=18.

Объяснение:

[tex]\displaystyle\\\left \{ {{a_2+a_4=16} \atop {a_1*a_5=28}} \right. \ \ \ \ \ \ d < 0\ \ \ \ \ \ \ S_9=?\\\\\\\left \{ {{a_1+d+a_1+3d=16} \atop {a_1*(a_1+4d)=28}} \right.\ \ \ \ \ \ \left \{ {{2a_1+4d=16\ |:2} \atop {a_1^2+a_1*4d=28}} \right.\ \ \ \ \ \ \left \{ {{a_1+2d=8} \atop {a_1^2+4a_1d-28=0}} \right. \\\\\\\left \{ {{2d=8-a_1\ |:2} \atop {a_1^2+4a_1d-28=0}} \right. \ \ \ \ \ \ \left \{ {{d=4-0,5a_1} \atop {a_1^2+4a_1*(4-0,5a_1)-28=0}} \right. \\\\\\[/tex]

[tex]\displaystyle\\\left \{ {{d=4-0,5a_1} \atop {a^2_1+16a_1-2a_1^2-28=0}} \right. \ \ \ \ \ \ \left \{ {{d=4-0,5a_1} \atop {-a^2_1+16a_1-28=0\ |*(-1)}} \right. \\\\\\\left \{ {{d=4-0,5a_1} \atop {a^2_1-16a+28=0}} \right.\ \ \ \ \ \ \left \{ {{d=4-0,5a_1} \atop {a^2_1-14a_1-2a_1+28=0}} \right.\\\\\\\left \{ {{d=4-0,5a_1} \atop {a_1*(a_1-14)-2*(a_1-14)=0}} \right.\ \ \ \ \ \ \left \{ {{d=4-0,5a_1} \atop {(a_1-14)*(a_1-2)=0}} \right. \\\\\\[/tex]

[tex]\displaystyle\\\\\left \{ {{d=-3\ \ \ \ d=3\notin} \atop {a_1=14\ \ \ \ a_1=2}} \right. \ \ \ \ \ \ \Rightarrow\ \ \ \ \ \ a_1=14\ \ \ \ d=-3.\\\\\\S_9=\frac{2*14+(9-1)*(-3)}{2} *9=\frac{28+8*(-3)}{2}*9= \frac{28-24}{2}*9=2*9=18.[/tex]