Answer to Question #349276 in Discrete Mathematics for sara

Question

. Show that the sequence {fn} defined explicitly by fn= 2(-4)n +3 is a

solution of the recurrence relation fn = -3 fn-1+4 fn-2.

3. Suppose that the discrete function f is defined recursively by:

f(0) =2 and

f(n+1) = 2f(n) +3

Then find f(1), f(2), f(3), f(4) and f(5)

4. Find a recursive definition for the following sequence

a. an = {2,4,8,16,32, …}, where n 1,

b. an ={3,6,9,12,15, … ) , where n 1,

5. Give a recursive definition of the sequence {fn} ,  if

(a) fn =5n (b) fn = 2n+1

(c) fn+1 = 10n (d) fn = 5.

6. Find the characteristic equation of each of the following recurrence

relations

a. fn = 3fn-1 -2fn-2, n > 2 with initial conditions: f1=3 and f2 = 7

b. yn= 6yn-1- 9yn-2, n>1, y0= 5 and y1= 3

7. Solve the following recurrence relations.

(a) an =5an-1 +6an-2, n  2 with a0 =1, a1= 3.

(b) 2an+2 –11an+1+ 5an = 0, n  0 with a0= 2, a1= -8.

(c) 3an+1= 2an+ an-1, n  1, a0 =7, a1 = 3

(d) an – 6an-1+ 9an-2 = 0, n  2, a0 =5, a1 =12.

Answer 1

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