Can a sequence be both arithmetic and geometric at the same time

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.