Question

The characteristic equation of the recurrence relation = c1−1 c2−2 ⋯ c− is obtained by substituting a. = b. = 2 c. = −2 d. = −

Certainly! Here's the complete question:
A)an=rn
B)an=r2
C)an=r−2
D)an=−

Answer 1

To derive the characteristic equation of a given recurrence relation, you substitute an = r^n and form a polynomial equation set to zero. The correct choice for the substitution is (A) an = r^n.

Step-by-step explanation:

To find the characteristic equation of a recurrence relation such as an = c1an-1 + c2an-2 + … + ckan-k, you typically substitute an = rn into the relation. This substitution assumes that the terms of the sequence can be expressed as powers of a base r. Then by collecting terms involving the same power of r, the characteristic equation is formed, which is usually a polynomial set equal to zero. The roots of this polynomial give the values for r that satisfy the relation. In this context, the correct substitution to obtain the characteristic equation would be (A) an = rn.