Trial and error in progression ?

Find the number of arithmetic progressions of at least 3 natural numbers with initial term 3 and whose sum is a three-digit number whose digits form a non constant G.P.

By non constant G.P, the geometric progressions are meant where the common ratios are not equal to 0 or 1 or the initial terms are not equal to 0. Constant G.P are the sequences {a,a,a, ......., a}, {a,0,0,.....0} and {0,0,0,...,0} with common ratios being equal to 1 and 0 in the former two respectively and the initial term being equal to 0 in the third one

Note: This problem is not created by me.