Let a,b be distinct real numbers and k,m be positive integers k+m=n≥3,k≤2m,m≤2k. Consider sequences x1,…,xn with the following properties:
(i) k terms xi, including x1, are equal to a;
(ii) m terms xi, including xn, are equal to b;
(iii) no three consecutive terms are equal.
Find all possible values of xnx1x2+x1x2x3+⋯+xn−1xnx1. inequalitiesceiling functionfloor functionalgebra unsolvedalgebra