The correct sequence of ecosystems in order of decreasing productivity is

1. Mangroves > 2. Grasslands > 3. Lakes > 4. Oceans

Mangroves: These coastal ecosystems boast exceptionally high productivity due to several factors. They receive rich nutrients from both land and sea, have a warm climate, and benefit from tidal flushing that brings in fresh nutrients and removes waste products.

Grasslands: These moderate-productivity ecosystems are characterized by abundant grasses and herbaceous plants. Their productivity depends on factors like rainfall, soil quality, and grazing pressure.

Lakes: Freshwater lakes exhibit varying levels of productivity depending on the nutrient availability (oligotrophic - nutrient-poor, eutrophic - nutrient-rich). Generally, they are less productive than mangroves and grasslands.

Oceans: Marine ecosystems, particularly open oceans, have the lowest overall productivity. Nutrient availability is limited in vast stretches of the ocean, leading to a slower rate of organic matter production compared to the other ecosystems listed.