Principal.cs

using System;
using System.Windows.Forms;

namespace R707DesplazarListBox
{
    public partial class Principal : Form
    {
        public Principal()
        {
            InitializeComponent();
        }

        private void btnAgregarElementos_Click(object sender, EventArgs e)
        {
            for (int i = 1; i <= 20; i++)
            {
                lbxElementos.Items.Add("Elemento no. " + i.ToString());
            }

            lbxElementos.TopIndex = lbxElementos.Items.Count - 1;
            lbxElementos.SelectedIndex = lbxElementos.Items.Count - 1;
        }
    }
}