One possibility is that there is too much friction in the cable where it passes through housing and stops, so that the derailleur spring cannot pull it through to reach 7th.

p.s. I somehow did not see that you apparently only have 7 cogs. FD's analysis below definitely applies, I would say to first loosen the shift cable and see if the derailleur then shifts to the small cog by pushing it in by hand then letting go. If so the problem is friction, if not it's adjustment or bending in of the hanger. If the derailleur is bent then on your 1st gear in the back the derailleur will be trying to shift past it.