If a₁, a₂, a₃……. Are in AP and ${\mathrm{a}}_4+{\mathrm{a}}_8+{\mathrm{a}}_{12}+{\mathrm{a}}_{16}=224$. Then the sum of first nineteen terms is _____________.

$\begin{array}{l}\left({\mathrm{a}}_4+{\mathrm{a}}_{16}\right)+\left({\mathrm{a}}_8+{\mathrm{a}}_{12}\right)=224\\ Let {\mathrm{a}}_4+{\mathrm{a}}_{16}={\mathrm{a}}_8+{\mathrm{a}}_{12}=\mathrm{k}\Rightarrow \mathrm{k}=112\\ \therefore {\mathrm{a}}_1+{\mathrm{a}}_2\dots \dots +{\mathrm{a}}_{19}=\left(a_1+a_{19}\right)+\left(a_2+a_{18}\right)+.....\left({\mathrm{a}}_8+{\mathrm{a}}_{12}\right)+\left(a_9+a_{11}\right)+a_{10}\\ =9\mathrm{K}+{\mathrm{a}}_{10}=9\left(112\right)+56=1064\end{array}$