1. A constant number isn't being added so it's not arithmetic. To get from 2 to 7, you'd be multiplying by 7/2 or 3.5. To get from 7 to 27, you'd be multiplying by 27/7 or 3.85. This means that there isn't a constant rate so it's not geometric either. This one is neither.
2. 16 divided by 4 is 4, 4 divided by 4 is 4, 1 divided by 4 is 1/4, so this one is geometric with a constant of 4.
3. To get from 71 to 62, subtract 9. To get from 62 to 53, subtract 9. This means that it's arithmetic with a constant of 9.
