The APs 100, 96, 92, ... and 20, 24, 28, ... have equal nth terms for one value of n. Which term is it, and what is its value?

First AP: $100+(n-1)(-4)=104-4n$. Second AP: $20+(n-1)4=16+4n$. Setting them equal, $104-4n=16+4n$ gives $88=8n$, so $n=11$ and the common value is 104 - 44 = 60 (and 16 + 44 = 60). The 10th terms are 64 and 56, the 12th terms are 56 and 64 - close, but not equal.