User talk:Larry keju

Let {x_n } be a sequence in R defined by : x_1=a,  x_2=b and x_(n+2)=1/2 (x_(n+1)+x_n ),  n ≥ 1. Define u_n=x_(n+1)-x_n. Prove that {u_n } is a geometric progression in R. Deduce that {x_n } is a Cauchy sequence in R.