15．（2022•沙河口区校级模拟）已知函数$f(x)=\frac{1}{3}x^{3}+4x$，记等差数列$\{a_{n}\}$的前$n$项和为$S_{n}$，若$f(a_{1}+2)=100$，$f(a_{2022}+2)=-100$，则$S_{2022}=($　　$)$