Each successive value in the sequence is formed by adding a number between 1 and 9. Given that Xn is odd we can not add an odd number so Xn+1-Xn = 2,4,6 or 8.
Let's define the symbol ? to be a generic odd digit, So ???2 is the four digit number with three odd digits and ends in 2.
First argue that one of the terms must have the form:
??2, ??4, ??6 or ??8
The next term is odd!