No, photosynthesis is not a cycle. Although its some of the events are cyclic. But overall it is not a cycle. Cycle starts from the same point and ends at the same point without needing new resources each time it starts. But each photosynthetic reaction requires new molecules of carbon dioxide and water to prepare the food. Photosynthesis is a process by which plants make their food by themselves from carbon dioxide and water in presence of sunlight and chlorophyll.