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Determine which of these are linear homogeneous recurrence relations with constant coefficients. Also, find the degree of those that are.

  1. $a_{n} = 3a_{n-2}$ 
  2. $a_{n} = 3$ 
  3. $a_{n} = a^{2}_{n−1}$ 
  4. $an = a_{n−1} + 2a_{n−3}$ 
  5. $an = a_{n−1}/n$ 
  6. $an = a_{n−1} + a_{n−2} + n + 3$ 
  7. $a_{n} = 4a_{n−2} + 5a_{n−4} + 9a_{n−7}$

1 Answer

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a) This is a linear homogeneous recurrence relation with constant coefficients of degree 2.

b) This recurrence is not homogeneous  because constant on right side

c) This recurrence is not linear. because of power $a_{n-2}^{2}$

d) This is a linear homogeneous recurrence relation with constant coefficients of degree 3.

e) This recurrence does not have constant coefficients so not linear 

f) This recurrence is not homogeneous.

g) This is a linear homogeneous recurrence relation with constant coefficients of degree 7.

 

for more detail you can follow this link

https://gateoverflow.in/339065/kenneth-rosen-edition-7th-exercise-8-2-question-1-page-no-524

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