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

Chapter 5, Problem 2

(choose chapter or problem)

Which of the following are second-order linear homogeneous recurrence relations with constant coefficients?

a. \(a_{k} = (k − 1)a_{k−1} + 2ka_{k−2}\)

b. \(b_{k} = −b_{k−1} + 7b_{k−2}\)

c. \(c_{k} = 3c_{k−1} + 1\)

d. \(d_{k} = 3d^{2}_{k−1}+ d_{k−2}\)

e. \(r_{k} = r_{k−1} − 6r_{k−3}\)

f.\(s_{k} = s_{k−1} + 10s_{k−2}\)

Text Transcription:

a_k = (k − 1)a_k−1 + 2ka_k−2

b_k = −b_k−1 + 7b_k−2

c_k = 3c_k−1 + 1

d_k = 3d^2_k−1+ d_k−2

r_k = r_k−1 − 6r_k−3

s_k = s_k−1 + 10s_k−2