If we consider the above fornula for E_n, how can it be that the energy level n=-1 is higher than the level for n=1? This should not be the case right
This is is from lecture nearly free electron model question 2
n is only a label for different states. A priori there is no relation between label n and energy E_n, the relation is only given once you name the states and calculate their energies.
Ah sorry, did you mean that the labels in the y-axis do not correspond to the values given by the formula
?
Yes I meant that 
yes the labels are indeed confusing, I am not sure what k_0 they used but it doesn’t seem consistent.