Final answer:
The nurse should suggest a nursing center for the 70-year-old dementia patient who can no longer live alone.
Step-by-step explanation:
Based on the information provided, the nurse should suggest Option 3: A nursing center because home care is no longer safe when discussing health care services and long-term living arrangements for the 70-year-old patient with worsening dementia. This option would provide the necessary support and care that the patient needs, considering their cognitive decline and inability to live alone. Nursing centers are equipped with trained staff who can provide round-the-clock assistance and ensure the safety and well-being of the patient.