Седьмой член арифметической прогрессии равен 19, а сумма первых девятнадцати членов равна...

a_1+6d=19\\ S_{19}=475,\ => \dfrac{2a_1+18d}{2}*19=475\ => \\\\ \left\{\begin{matrix} a_1+6d=19 \\ 19(a_1+9d)=475 \end{matrix}\right. <=> \left\{\begin{matrix} a_1+6d=19 \\ a_1+9d=25 \end{matrix}\right. <=>\\ \left\{\begin{matrix} 3d=6 \\ a_1=19-6d \end{matrix}\right. <=> \left\{\begin{matrix} d=2 \\ a_1=19-12=7 \end{matrix}\right. " alt="a_7=19,\ => a_1+6d=19\\ S_{19}=475,\ => \dfrac{2a_1+18d}{2}*19=475\ => \\\\ \left\{\begin{matrix} a_1+6d=19 \\ 19(a_1+9d)=475 \end{matrix}\right. <=> \left\{\begin{matrix} a_1+6d=19 \\ a_1+9d=25 \end{matrix}\right. <=>\\ \left\{\begin{matrix} 3d=6 \\ a_1=19-6d \end{matrix}\right. <=> \left\{\begin{matrix} d=2 \\ a_1=19-12=7 \end{matrix}\right. " align="absmiddle" class="latex-formula">
$a_5+a_{12}+a_{20}=a_1+4d+a_1+11d+a_1+19d=3a_1+34d=\\ =3*7+34*2=21+68=89.$