Which answer describes the type of sequence?

1, 3, 5, 7, ...

arithmetic

neither arithmetic nor geometric

geometric

can someone show me how to do this?

To be arithmetic, you have to have the same difference between all pairs of consecutive terms. You don't. You have differences of - 4, 8, - 16 ...

To be geometric, you have to have the same ratio between all pairs of consecutive terms. You don't. You have ratios of - 3, - 5/3, - 7/5 ...

To have a series that is both arithmetic and geometric, all the terms have to be equal.

This series is neither arithmetic nor geometric.