A real sequence {xn}1∞ which satisfies the recurrence xn+1=axn+bcxn+d, in which all of
a,b,c,d are real will, for certain values of these constants, be divergent. It is the purpose of this
note to examine the limit
limN→∞1N∑n=1Nf(xn):f∈C(−∞,∞)
in these cases. Except for certain exceptional values of a,b,c,d this value is found for almost all
x1.