Some numerical experiments with the sequence x_n determined by the updating law:
x_(n+1)  =  125 +  .6 x_n

x[1]  =  125
x[n_]  :=  125  +   .6*x[n - 1]

TableForm[Table[{n,  x[n]},  {n,  1,  50}]]

ListPlot[
      Table[{n,  x[n]},  {n, 1, 30}]]

Some algebraic experiments with the sequence  x_n :

x[1]  =  125;
x[n_]  :=  125  +   m*x[n - 1]

x[2]
x[3]
x[4]

Simplify[x[3]]
Simplify[x[4]]
Simplify[x[17]]

A new updating law:

y[1]  =  125;
y[n_]  :=  
      125  +  (1  +   .06*Cos[((2  Pi n)/28)]) ( .6) 
          y[n - 1]

TableForm[Table[{n,  y[n]},  {n,  1,  50}]]

ListPlot[
      Table[{n,  y[n]},  {n, 1, 30}]]

ListPlot[Table[{n,  y[n]},  {n, 1, 100}]]