Which of the following are second-order linear homogeneous recurrence relations

Question

Which of the following are second-order linear homogeneous recurrence relations with constant coefficients? Circle all that apply. Please include an explaination of why it is 'second-order linear homogenous recurrence relations with constant coefficients' thank you so much.

4. (28) Which of the following are second-order linear homogeneous recurrence relations with constant coefficients? Circle all thatapply 2a 5a a. a k-1 k-2 b. b k-1 k-2 C. C k-1 k-2 d. d 3d k-2 k-1 e. r k-1 k-2 100s f s k-2 2u g. u k-1

Explanation / Answer

second-order linear homogeneous recurrence relations with constant coefficients

Let x[n] be a sequence

1) Second order means ,x[n] , x[n+1] and x[n+2] are related .(with the coefficients for x[n+2] and x[n] non-zero).

2) homogeneous , linear, only constant coeffients should appear for the unknowns x[k] and there should not

be any non-zero constant term (for example in e) above the constant term is -2. so the relation is not homogeneous)

3) recurrence ,. the relationship between x[1], x[2] ,x[3] is the same as that between x[2],x[3],x[4] and so on (the relationshiip or the equation recurs)

The ones that fit the description are a,b , d and f

NOTE:

c) not linear. no squares and higher powers should occur

e) non-zero constant terms

g) is of first order

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