How do I know if a sequence is arithmetic, geometric, or neither

Step-by-step explanation:

Let's assume that you have a sequence written out in always increasing or always decreasing order.

If each new term is equal to the previous term, plus a certain constant, then the sequence is arithmetic. Example: 2, 7, 12, 17, 22, ... (the additive constant is 5).

If each new term is equal to the previous term, multiplied by a certain constant, then the sequence is geometric. Example: 2, 8, 32, 128, ... (the multiplicative constant is 4).

If the spacing between terms is not a constant, then the sequence is neither arith. nor geom.

If all new adjacent terms are not found by multiplying the previous term by the same constant, the sequence is not geometric (and not arithmetic).