Let A1 2 A N 1 5 A N 4 A N For N 1

let a1 = 2, a(n+1) = (5*a(n) – 4) / a(n) for n>=1. Show that (1 <= a(n) <= a(n+1) <= 4) for n>=1

Given,A(n+1) = 5*A(n) -4/A(n) A(n+1) = 5 – [4/A(n)]That can be written as[A(n+1) – 1]/4 = 1 – [1/A(n)]Putting A(1) = 2A(2)&gt; 1From A(2) ,A( 3) &gt;1This tells that A(n) &gt; 1A(n+1)…