The circuit section consists of four series-connected resistors, the resistances of which are equal to r, 2r, 3r and 4r.

The circuit section consists of four series-connected resistors, the resistances of which are equal to r, 2r, 3r and 4r. What should be the resistance of the fifth resistor added to this section in series with the first four in order for the total resistance of the section to increase 3 times?

When resistors are connected in series, their resistance is added, i.e. the resistance of the circuit section will be equal to R = 1 + 2 + 3 + 4 = 10 ohms. To increase this resistance by 3 times, the fifth resistor must have a resistance of 20 ohms:
R2 = R + 20 = 10 + 20 = 30 Ohm