Final answer:
There is no specific ancient Greek word to distinguish a female graduate of Alpha Sigma Alpha. The term should theoretically end in a vowel associated with feminine nouns according to Greek grammar, but in current English usage, both male and female graduates are commonly referred to as alumni.
Step-by-step explanation:
The term for a female graduate of Alpha Sigma Alpha will apply the general grammatical understanding of ancient Greek, where distinct endings in the language indicate the gender of nouns. The term should end in a vowel that is traditionally associated with feminine nouns, such as eta (η) or omega (ω), as per ancient Greek grammar rules.
In modern terms, however, there is no specific word that distinguishes a female graduate of Alpha Sigma Alpha from a male graduate. Both are generally referred to as alumni. In addressing the given example, using an ancient Greek noun ending to construct such a term would be speculative and not conforming to contemporary usage. Current usage of language associated with Greek-letter organizations such as sororities does not strictly adhere to ancient Greek grammatical rules, particularly when it comes to titles for graduates. Therefore, it would be better to use the gender-neutral 'alumnus/alumni' or specify 'female alumnus' for clarity when needed.