The mode of a discrete random variable X with pmf px is that

The mode of a discrete random variable X with p.m.f. p(x) is that
value x* for which p(x) is largest (the most probable x value).

Consider X {# failures before the 1st success}, distributed geometric(p)
... determine the mode of this distribution.

Solution

Failures before first success can take values 0,1,2,3,,,,,,,,

Thus each positive number including 0 will occur only once in this distribution.

MOdes are all integers starting from 0.