the numbers of first 8 beads which are white are
1,5,9,13,17,21,25,29
think of it as an arithmetic progression here the first term will be 1 cause white was first bead then after 3 blue beads another white added soits position is fifth now the difference would come out as 5-1=4 so now position of next white bead could be predicted by nth term formula of an AP which a+(n-1)d here a is first term which in this case is one and d is difference which here is 4
So nth bead position is 1+(n-1)4