You are correct. The correct sequence of ecosystems in the order of decreasing productivity is:

1. Mangroves

2. Grasslands

3. Lakes

4. Oceans

Mangroves have high productivity due to the unique adaptations of mangrove trees and the nutrient-rich environment of coastal areas. Grasslands have a relatively lower productivity compared to mangroves. Lakes have lower productivity compared to both mangroves and grasslands. Oceans, although vast and supporting diverse ecosystems, have the lowest productivity among the given options due to the limited availability of nutrients and sunlight in the open water.