Something

private void ColorizeDataGridView()
{
    int numRows = dataGridView1.Rows.GetRowCount(DataGridViewElementStates.None);
    for (int i = 0; i < numRows; i++)
    {
        // Determine the alternating background color.
        DataGridViewCellStyle dsg = new DataGridViewCellStyle(dataGridView1.Rows[i].DefaultCellStyle); // Get old style before modifying the background color.
        if (i % 2 != 0)
        {
            dsg.BackColor = Color.FromArgb(255, 239, 239, 239); // Light Gray
        }
        else
        {
            dsg.BackColor = Color.FromArgb(255, 255, 255, 255); // White
        }

        // Apply the new background color and header text.
        dataGridView1.Rows[i].DefaultCellStyle = dsg;
        dataGridView1.Rows[i].HeaderCell.Value = Convert.ToString(i + 1);
    }
}