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[المسافر]

Question-1: (15 marks)
(a) (4 marks) : Suppose that {-4, a,-12} are the first 3 terms of an arithmetic sequence {Xn }, n=1, 2, 3….
(i) Find the value of a and write a recurrence relation for {Xn }.




(ii) Write the closed form for {Xn } .




(b) (4 marks) : Suppose that {-4, b,-12} are the first 3 terms of a geometric sequence {Yn } , n=1, 2, 3….
(i) Find the value of b and write a recurrence relation for {Yn }.



(ii) Write the closed form for { Yn}.




(c) (4 marks) : Let {36, 0, 12} be the first 3 terms of a linear recurrence sequence {Zn }, n = 1, 2, 3….
(i) Find the parameters of the sequence and hence write its closed form.



(ii) Determine the long term behavior of { Zn}.