Adam Clarke on Acts 3:25

Ye are the children of the prophets - This is the argumentum ad hominem: as ye are the children or disciples of the prophets, ye are bound to believe their predictions, and obey their precepts; and not only so, but ye are entitled to their promises. Your duty and your interest go hand in hand; and there is not a blessing contained in the covenant which was made with your fathers but belongs to you. Now, as this covenant respected the blessings of the Gospel, you must believe in Jesus Christ, in order to be put in possession of all those blessings.