A linear difference equation can be written in terms of "differences", ( , , etc.) or in terms of different subscripts: , , etc.. The "order" of a difference equation is, in the first case, the largest power of and, in the second, the largest "n".
For example is a third order equation because of the .
Since , , and that same equation can be written as . That, again, has order 3 because of the "n+3".
I don't understand the "e.g.". Knowing the order does not greatly help in solving the equation. There are a large variety of ways of solving such equations.eg.so how would I determine (if I am finding for n+1 or not)the long term chance of survival after contracting a deadly virus.