Some bacteria like BGA are called autotrophic bacteria because they can synthesize their food (organic substances) through various sources such as light and chemicals.
BGA is a group of photosynthetic bacteria. These are also called cyanobacteria.
These have photosynthetic pigments, so they can absorb solar energy and synthesize organic substances.
Some bacteria are called chemoautotrophic as they can synthesize their food the rough chemicals.
Chemoautitrophic bacteria use inorganic substances like nitrate, ammonia, methane and molecular hydrogen.
For example, Methanomonas bacteria use methane as the source of carbon and energy.
Heterotrophic nutrition:
Heterotrophic nutrition is also found in bacteria.
Some bacteria depend on other organisms for nutrition.
These are found as parasites, saprophytes and symbiotic bacteria.
Parasites are found in other organisms and infect the host cell. Even some of these are disease-causing in plants and animals.
Saprophytes absorb nutrition from dead organisms or organic substances.
Some bacteria live in symbiotic relationships with other organisms.
For example, some nitrogen-fixing bacteria like Rhizobium are found in the roots of leguminous plants.
Final answer: Mode of nutrition in bacteria are both autotrophic and heterotrophic.