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This is one of my method in my custom adapter class,

@Override
public Object instantiateItem(ViewGroup container, final int position) 

 layoutInflater = (LayoutInflater) context.getSystemService(Context.LAYOUT_INFLATER_SERVICE);
 View view = layoutInflater.inflate(R.layout.custom_layout, null);
 ImageView imageView = (ImageView) view.findViewById(R.id.imageView);
 imageView.setImageResource(images[position]);

 if((position) == (images.length-1))
 // Start another activity using intent
 

 ViewPager vp = (ViewPager) container;
 vp.addView(view, 0);
 return view;

and how to start new activity in this custom adapter class method?

To start another activity you simply need a context

Intent intent = new Intent(ctx, YourNewActivity.class)
ctx.startActivity(intent);

You shouldn't start an activity in the adapter... the adapter should receive an interface (in the constructor would be the best) which would notify the Fragment or Activity that an item was clicked and then they could start the other Activity, check this example:

https://android.jlelse.eu/click-listener-for-recyclerview-adapter-2d17a6f6f6c9

Good luck 🙂