A real wall is a sandwich: cladding, sheathing, insulation, a vapour control layer, gypsum, paint. Every watt that leaves the room crosses all of them, one after another, in a queue. That is what in series means, and it makes the arithmetic almost insultingly simple. $R_{tot} = R_1 + R_2 + R_3$ — read aloud R-total equals R-one plus R-two plus R-three.

The subscripts are just the layers, numbered in the order the heat meets them: $R_1$ is the first layer's R-value, $R_2$ the second, $R_3$ the third, and $R_{tot}$ — R-total — is the whole assembly. All four are in m²·K/W, and the sum only works because every layer covers the same area.

Now the mistake this lesson exists for. A wall has two layers you cannot see and cannot buy: the air films clinging to its inside and outside faces. Still indoor air is worth about RSI 0.12; the windswept outside face about RSI 0.03. Small numbers, and they are the difference between a calculation that matches the building and one that does not. Films are layers. Count them.

One warning from the electrical bench. Resistors sharing the same two terminals add as reciprocals, $\dfrac{1}{R_{tot}} = \dfrac{1}{R_1} + \dfrac{1}{R_2}$, and that rule is right — for PARALLEL paths. It is the wrong rule here, and it will hand you a total smaller than your smallest layer, which no queue of resistances can ever be. Series adds. Parallel reciprocates. The studs in two lessons' time are the parallel case, and we will do them properly there.