How do I deduce the sign for the restoring forces in a system of N masses connected by N+1 springs?

Suppose we have a system of $N$ masses connected by $N+1$ springs, where the stiffness of the springs alternates between $k$ and $2k$. We assume N to be an even number. Determine the forms of the equations of motion.

In lieu of a picture, the system I’m presented with can be explained by saying that if a mass has an even position in the chain, then the spring to its left has a spring constant of $2k$ and the spring to its right has a spring constant of $k$, vice verse for springs with odd positions.

Here is my issue: I don’t understand where the signs on the spring constants come from in the equations of motion.

An example of one equation is $mddot{x}_1=-k(x_1)+2k(x_2-x_1)$ where $x_i$ represents the displacement of a mass $i$ from its equilibrium position and $(x_2-x_1)$ represent a contraction of a spring by $x_1$ and an extension on the same spring by $x_2$. Where does the positive sign on the $2k$ come from? If we take a look at the mass for this equation which I will call $M_1$, if I move said mass from its equilibrium position then the forces applied by the springs on either side of the mass are acting against my movement away from the equilibrium position, should this not imply a negative sign on both the $k$ and the $2k$?

EDIT: The ends of the end-springs are connected to walls.