Using w to denotate white beads and b for blue beads, the pattern is wbbb wbbb wbbb...Then the beads that are white are the numbers 1, 5, 9 13, 17, 21, 25, 29,...The rule is the general term of an arithmetic progression with first term 1 and difference between contiguous terms equal to 4. An = Ao + d (n-1) = 1 + 4(n-1)