A family of transmissions includes three planetary gearsets and five torque-transmitting mechanisms. Each family member may be employed in a powertrain to provide six forward speed ratios and one reverse speed ratio when the torque-transmitting mechanisms are engaged in combinations of two in a selected manner. Each planetary gearset includes three planetary members. The first member of the first planetary gearset is continuously connected with the first member of the second planetary gearset. The second member of the first planetary gearset is continuously connected with a first member of the third planetary gearset. The second member of the second planetary gearset is continuously connected with the second member of the third planetary gearset. An input shaft is continuously connected with one of the members of the planetary gearsets and an output shaft is continuously connected with another member of the planetary gearsets.