1. The problem statement, all variables and given/known data Two sequences are defined by Xn+1 = 3Xn + 4Yn ; Yn+1 = 2Xn + 3Yn What is the approximate value of Xn/Yn as n increases? 2. Relevant equations none 3. The attempt at a solution My solution was to say that as n tends to infinity, both Xn, Yn tend to infinity therefore Xn/Yn tends to 7/5... on checking by calculating values this is completely wrong, infact Xn/Yn tends very quickly to root 2. Why?? EDIT: ok, not completely wrong, 1.4 isn't that far off root 2, but root 2 is such a neat number it feels like it should be possible to reach it using algebra.