Let k be a given positive integer. The sequence xn is defined as follows: x1=1 and xn+1 is the least positive integer which is not in {x1,x2,...,xn,x1+k,x2+2k,...,xn+nk}. Show that there exist real number a such that xn=⌊an⌋ for all positive integer n. floor functioninductionRecursive Sequences