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Pattern forming instabilities induced by ultralow frequency sinusoidal voltages were studied in a rodlike nematic liquid crystal by microscopic observations and simultaneous electric current measurements. Two pattern morphologies, electroconvection (EC) and flexodomains (FD), were distinguished, both appearing as time separated flashes within each half period of driving. A correlation was found between the time instants of the EC flashes and those of the nonlinear current response. The voltage dependence of the pattern contrast for EC has a different character than that for the FD. The flattening of at reducing the frequency was described in terms of an imperfect bifurcation model. Analyzing the threshold characteristics of FD, the temperature dependence of the difference of the flexoelectric coefficients was also determined by considering elastic anisotropy.