Arithmetic Progressions
Pyth, 30 bytes

?tJ{-VtQQ"NAAP"+hJ%"n%+d"-hQhJ


Test suite

To check whether it's a arithmetic procession, this uses a vectorized subtraction between each element and the previous, -VtQQ. A ternary checks if there are multiple values in the result (?tJ{) and prints NAAP if so. Then, to get the + or - right, the mod-formating %+d is used.