Explanation:
Productivity in an ecosystem refers to the rate at which organic matter is produced by photosynthesis or chemosynthesis. The correct sequence of ecosystems in the order of decreasing productivity is:

Mangroves, grasslands, lakes, oceans

Here's why:

1. Mangroves: Mangroves are highly productive ecosystems found in tropical and subtropical regions. They are characterized by the presence of salt-tolerant trees and shrubs that form dense forests along the coastline. Mangroves are highly productive because of the following reasons:

- They receive abundant sunlight due to their location in the tropics.
- They have high nutrient availability due to the deposition of organic matter from the sea and the rivers.
- They have a high rate of photosynthesis due to the presence of specialized adaptations in the plants, such as salt glands and pneumatophores.

2. Grasslands: Grasslands are ecosystems dominated by grasses and other herbaceous plants. They are found in temperate and tropical regions and are characterized by a dry and windy climate. Grasslands are highly productive because of the following reasons:

- They have a high rate of photosynthesis due to the abundance of sunlight and the absence of trees that compete for light.
- They have a high nutrient availability due to the decomposition of organic matter by microbes in the soil.
- They have a high rate of biomass production due to the rapid growth of grasses and other herbaceous plants.

3. Lakes: Lakes are freshwater ecosystems that vary in size and depth. They are highly productive because of the following reasons:

- They receive abundant sunlight that penetrates the water column and reaches the submerged plants.
- They have a high nutrient availability due to the deposition of organic matter from the surrounding land and the inflow of nutrients from rivers and streams.
- They have a high rate of biomass production due to the rapid growth of algae and other aquatic plants.

4. Oceans: Oceans are the largest and most diverse ecosystems on Earth. They are highly productive in certain areas, such as coral reefs and upwelling zones, but overall, they have a lower productivity compared to the other ecosystems listed above. The reasons for the lower productivity in oceans are:

- They have a lower nutrient availability due to the low concentration of nutrients in the water column.
- They have a lower rate of photosynthesis due to the limited penetration of sunlight in the water column.
- They have a lower rate of biomass production due to the slow growth of phytoplankton and other aquatic organisms.

In conclusion, the correct sequence of ecosystems in the order of decreasing productivity is mangroves, grasslands, lakes, and oceans.