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

Chapter 5, Problem 1

(choose chapter or problem)

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

a. \(a_{k} = 2a_{k−1} − 5a_{k−2}\)

b. \(b_{k} = kb_{k−1} + b_{k−2}\)

c. \(c_{k} = 3c_{k−1} \cdot c^{2}_{k−2}\)

d. \(d_{k} = 3d_{k−1} + d_{k−2}\)

e. \(r_{k} = r_{k−1} − r_{k−2} −2\)

f.\(s_{k} = 10s_{k−2}\)

Text Transcription:

a_k = 2a_k−1 − 5a_k−2

b_k = kb_k−1 + b_k−2

c_k = 3c_k−1 cdot c^2_k−2

d_k = 3d_k−1 + d_k−2

r_k = r_k−1 − r_k−2 −2

s_k = 10s_k−2