Suppose I have an arithmetic sequence.

a+ (a+d) +a(a+2d)......

Here d is greater thanzero. I want mod this arithmetic sequence with M.

(a)%M + (a+d)%M + (a+2d)%M +(a+3d)%M................ Now I want to know, Any cycle will be created? If create when and why? How can I figureout the cycle?

Sorry for my bad english.