Can a sequence be both arithmetic and geometric? Explain why.

The only way is that the sequence is a constant number, for example,

3, 3, 3, 3, 3, 3 ...

It is arithmetic with differece 0 and geometric with ratio 1.

To prove it, figure a general arithmetic sequence:

, A1, A1 + d, A1 + 2d, A1 + 3d, A1 + 4d, ...

And a general geometric sequence:

A1, A1*r, A1*2r, A1*3r, A1*4r, ...

They are equal if and only if

A1 + d = A1*r, and A1 + 2d = A1*2r and A1 + 3d = A1*3r, ...

Which only happens if d = 0 and r = 1, i. e. the numbers in the sequence are a constant: A1, A1, A1, A1, ...