Yes, it can both arithmetic and geometric.
The formula for an arithmetic sequence is: a(n)=a(1)+d(n-1)
The formula for a geometric sequence is: a(n)=a(1)*r^(n-1)
Now, when d is zero and r is one, a sequence is both geometric and arithmetic.
This is because it becomes a(n)=a(1)1 =a(1). Note that a(n) is often written an
It can easily observed that this makes the sequence a constant.