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1.Letak = 3" + k_ 2forallk 2 0. a. Write down the values of a1, 32 and (13. b. Write down the values of 14(1): A(2) and A(3) dened by the recurrence relation: Am) = 1,A(k) = 3A(k 1) 218 -l- 7,31\" 21 c. Show that AUc) = 0:: is a solution of the recurrence relation for all values ofk 2 1. 2. Write down all derangements of the set {(1, b, c, d} and show that the number of derangements is the same as predicted bythe recurrence D(") = (n 1)(D(n 2) + D(n 1))with initialvaluesD(1) = UandD(2) = 1. Hint: a derangement is a permutation of an ordered set where no element is in the same place as before. Example: {I}, a, d, c} is a derangement of{a, b, c, d} because all of the letters positions have changed. 3. Solve the recurrence relation A(n) = 6A(n, 1) 11A(n 2) + 6A(n 3) subject to initial values 14(1) = 25 A(2) = 6, A(3) = 20. Hint: See example 2.4.6 on page 141 of the course text