Question

Which is the term for the state in which someone needs more of a drug to produce the same effect

Answer 1

This is a term known as tolerance. Tolerance is an extremely dangerous aspect of illicit and even medicinal drug use for one reason; It is a mental issue, instead of more than a physical issue... however it is one that affects the physical body. Because a patient can develop a tolerance towards drugs, they may be pushed toward taking more of that drug, however this is dangerous for the physical body, because that is not where the drug has developed tolerance toward, so the more drugs they take, the more worse off the body will get. 

Answer 2

the term for the state in which someone needs more of a drug to produce the same effect is TOLERANCE