As the term ________ next week, the school will hold a special assembly for all students.
a. is finishing b. has finished
[. . .] Are they both correct?
No, they are not both correct. The "as"-clause would make no sense with the present perfect, which refers to the past. Something in the past can't be in the future ("next week").
With "is finishing," the "as"-clause is ambiguous in meaning. It could mean that the fact that the term is coming to a close is the reason for holding the assembly, or that the assembly will be held while the term is coming to a close.
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