Use the debugger and look at the "_newsarticleProvider" variable on the line that throws the error and you'll find it is null. At no point are you assigning a class to the variable, you're never creating an instance of ArticleProvider.
Create a constructor for your controller and in that constructor do
_newsarticleProvider = new ArticleProvider();
Alternatively look to use dependency injection, but that's a fairly advanced technique, maybe one you can come back to later.