sequences and series - Can a arithmetic progression have a common difference of zero & a geometric progression have common ratio one?

How many three digit numbers have the property that their digits taken from left to right form an Arithmetic or Geometric Progression?

Eg. 123 is in form a AP when the digits are taken from left to right(1,2,3)

*should I count the numbers like 111,222.......999??

Because in my book they are not mentioned but

"The common difference can be positive, negative or 'zero'. The English definition of the word 'progression' has nothing to do with the mathematical definition of arithmetic progression. Thus, a, a, a, a, a..... is a valid A.P. with c.d. 0.(It is also a geometric progression with common ratio=1."