Steady state solutions to recurrence relations

We can define the term values of a sequence by a recurrence relation of the form $t_{n+1}=rt_n+d$tn+1​=rtn​+d, where $t_1=a$t1​=a.

If $-1−1<r<1, then the term values approaches a steady-state solution in the long term, when $n$n becomes large.

Consider the recurrence relation $t_{n+1}=0.2t_n+8$tn+1​=0.2tn​+8 where $t_1=-4$t1​=−4.

Consider the recurrence relation $t_{n+1}=-0.8t_n-18$tn+1​=−0.8tn​−18 where $t_1=3$t1​=3.