Which type of rider specifically adds benefits for the insured's family members?

The appropriate choice for a rider that specifically adds benefits for the insured's family members is the family rider. A family rider allows the policyholder to extend life insurance coverage to the spouse and children, providing a lump-sum benefit upon the death of any covered family member. This rider is particularly beneficial for policyholders who want to ensure financial protection for their loved ones without needing separate policies for each family member.

In contrast, an accidental death rider focuses on providing additional benefits in the event that the insured dies due to an accident. The cost of living rider is designed to adjust the coverage amounts in alignment with inflation but does not specifically cover family members. Term riders provide temporary coverage but do not inherently include family members unless specified. The unique feature of the family rider is its explicit intent to include family members in the benefits, thus making it the most appropriate choice.