Force in a multiple spring system

[wahaj]

There are two springs attached together (the second spring begins where the first one ends) and they both have different value for spring constant. The total spring potential energy can be found by the following formula
$$\frac{1}{2}ks_1^2 + \frac{1}{2}ks_2^2$$
but to solve for s₁ and s₁ I saw the equation
$$F = ks_1 = ks_2$$
what is the logic behind the second equation? It seems to me that when we are finding the force in one spring we completely ignore the second spring.
In another situation consider two spring but this time there is a spring inside a spring and the spring that is inside has a different unstretched length that the one on the outside. How would I relate the total potential energy in this situation so I can find the maximum compression the springs will undergo in order to stop that object.

 

[Simon Bridge]

The second equation is incorrect.
It should be $k_1s_1=k_2s_2$ for unequal springs in series.
http://en.wikipedia.org/wiki/Series_and_parallel_springs