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Math 4140 Homework 2 Key Problem 1 Suppose that f(n) = 7f(n -1) -16f(n -2) + 12f(n -3) and that f(0)=2,
 

Summary: Math 4140 Homework 2 Key
Problem 1 Suppose that f(n) = 7f(n - 1) - 16f(n - 2) + 12f(n - 3) and that f(0)=2,
f(1)=5, and f(2)=11. Find a closed for for f(n).
Answer:
f(n) = 7f(n - 1) - 16f(n - 2) + 12f(n - 3)
r3
= 7r2
- 16r + 12
r3
- 7r2
+ 16r - 12 = 0
(r - 2)2
(r - 3) = 0
so
f(n) = A 2n
+ Bn 2n
+ C 3n
so
A + C = 2
2A + 2B + 3C = 5

  

Source: Ashlock, Dan - Department of Mathematics and Statistics, University of Guelph

 

Collections: Mathematics