When resistors are in series in an electric circuit, the currents flowing through the resistors are the same. Think of it as a chain of resistors, with no branching off. The current that enters the first resistor exits in full, then enters the next resistor, an so forth, until it enters and exits the last resistor, in full.
Given resistors R1, R2, R3, ... in series, and the same current I flowing through all, then by Ohm's law, the total voltage drop across the series is
IR1 + IR2 + IR3 + ... = I(R1 + R2 + R3 + ...)