the apple is moving in this way : (1+2+3+4+….)
so if the sum of (1+2+3+4+5+…) is divisible by the number of plates then the apple will reach the plate no 1

1 then 2 then 3 then 4 then 5 etc (how  moves go)
so position  of apple will be like,1,1+2,1+2+3,1+2+3+4,as every move goes (position from first plate)
so if we divide total by number of plates remainder will tell the position of apple at end .since sum  can be formalised into n(n+1)/2 where n is last value  of series .so the number of plates must be factor of n(n+1)/2 if we want it to end in first place.
so if number of plates is k then if i choose n=k square.(k^2)  so it will be.k^2(k^2 +1)/2 should be divisible by k and  it is divisible by k so it will always happen no matter how many plates it is always possible