Solution for Section 8.3 Question 1

1. Recall that a  second-order linear homogeneous recurrence relation with constant coefficients is a recurrence relation of the form
a_k = A · a_k-1 + B · a_k-2    for all integers k some fixed integer, where A and B are fixed real numbers with B 0.

a) a_k+1 = 4 a_k - ¹/₂ a_k-1     Yes.

b) b_k = - b_k-1 + 5   No, since the formula uses only one of the previous terms in the sequence instead of two.

c) c_k = a c_k-1 + c_k-2  Yes, since a is a constant.

d) d_k = d_k-1 d_k-2  No, since this is a product of two previous terms.

e) e_k = 2 e_k-1 + 3 e_k-2 - e_k-3   No, since the formula uses three previous terms in the sequence instead of two.

Back to Section 8.3