The correct order of stages a developing embryo goes through is Zygote; morula; blastocyst; gastrula.
After fertilization of the egg, the zygote is formed, which will go through successive stages of mitotic divisions and cell differentiation, until an individual is formed. These events are called embryogenesis, or embryonic development, and their stages are:
With this information, we can conclude that the correct order of stages a developing embryo goes through is Zygote; morula; blastocyst; gastrula.
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