6, 1, -4, -

is this sequence arithmetic or geometric? what's the common difference or common ratio? what is the recursive formula?

Texaschic nailed it when saying that it's arithmetic

The recursive way to write this is to say




which tells us "start at 6 and each time subtract off 5"

The  portion is the nth term while  is the term just before the nth term

Subtracting is the opposite of adding