in a series and reactive circuit what formula is used to find the total impedance?

 

If they are in series, then the total impedance is the sum of the individual impedances.

 

Answer to the question to which I suspect you actually wanted to ask:

Subtract the capacitive impedance from the inductive impedance to find the total impedance, then to find the total reactance take the square root of the sum of the square of the total impedance plus the resistance squared.

https://www.allaboutcircuits.com/textbook/alternating-current/chpt-5/series-r-l-and-c/

 

IF you are defining both capacitive and inductive REACTANCE as positive values (a very bad, though unfortunately common, practice) then this is what you would do. The far, far better definition is that reactance is the imaginary part of impedance, and thus capacitive reactance is negative while inductive capacitance is positive. As a result, you add reactances in series.

But IMPEDANCE is a concept that combines the magnitude and the phase information and therefore you always add impedances that are in series. This is regardless of whether you use complex impedance or whether you just use vector impedance.