Answer
Not a geometric sequence.
Work Step by Step
In order for a sequence to be geometric, the quotient of all consecutive terms must be constant.
Here: $a_1=1^2-1=1-1=0$
$a_2=2^2-2=4-2=2$
$a_3=3^2-3=9-3=6$
$a_4=4^2-4=16-4=12$
Thus we can see that the quotient is not constant, thus it is not a geometric sequence.