Pre-ます Form VERB + ませんか as “(Won’t you/Would you like to) VERB?”
This construct is predominantly used to make a suggestion towards some activity or to invite someone to engage in some activity, however in some cases it can be quite literally interpreted as a genuine negative-form question, such as:
Washington-sensei wa irasshaimasenka?
(Is Washington-sensei not here?)
This form is very similar to the ましょう-Form because both make efforts towards insisting upon a certain action, but this form can be interpreted as less assertive.
Kurasu no ato de crepes wo tabe ni shopping center ni ikimasenka?
(Would you like to go to the shopping center after school to eat crepes?)