1. The problem statement, all variables and given/known data A sequence (an) of real numbers is defined by a(1) = 6, a(n) = (1/4)(2*a(n−1) − 3) for n >= 2. where n is a natural number show the sequence is monotonically decreasing 2. Relevant equations None 3. The attempt at a solution I tried to prove it by induction. Let P(n) be the predicate that a(n) < a(n-1) base case p(2)... a(1) = 6 a(2) = (1/4)*(2*6-3) = 9/4 a(2) < a(1) ..... base case is true induction step assume p(k) to be true a(k) < a(k-1) now we try to prove p(k+1) is true using or assumption about p(k) a(k+1) = (1/4)*(2(k) - 3) rearranging a(k) = 2*a(k+1) - 3 using our assumption a(k-1) < 2*a(k+1) - 3 I'm not sure where to go from here I can't think of anyway of relating a(k) and a(k+1) with an inequality. any help would be appreciated.