The word progeny is defined as
A descendant or the descendants of a person, animal, or plant;
offspring
by Oxford Dictionary.
My question is that if I can use it instead of "children" to sound formal as in the following contexts.
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Second hand smoking has pernicious effects on progenies if their parents smoke in the home.
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Two out of three progenies in Africa are left out of secondary school.
or the word can only suitable for using in a context in which there is reference to the relationship between parents and children.
Best Answer
Progeny is generally used as an uncountable noun.
"My progeny" could refer to 1 child, or to 8 children, 29 grandchildren, and 95 great-grandchildren.
In your two examples, you are trying to use progeny as a countable noun. It's incorrect to do so. "Children" is formal enough to use in your two examples.