Question

give first four terms and identify whether the given recurrence relation is linear homogenous or not. if the relation is a linear homogenous relation, give its degree. a. an=2.5an-1, a1=4 b. bn=-3bn-f1-2bn-2, b1=-2, b2=4​

Answer 1

Answer:

Explanation:

Linear recurrence:

Each term of a sequence is a linear function of earlier

terms in the sequence.

For example:

a0 = 1 a1 = 6 a2 = 10

an = an-1 + 2an-2 + 3an-3

a3 = a0 + 2a1 + 3a2

= 1 + 2(6) + 3(10) = 43

3

Linear recurrences

Linear recurrences

1. Linear homogeneous recurrences

2. Linear non-homogeneous recurrences

4

Linear homogeneous recurrences

A linear homogenous recurrence relation of degree k with

constant coefficients is a recurrence relation of the form

an = c1an-1 + c2an-2 + … + ckan-k,

where c1, c2, …, ck are real numbers, and ck0.

an is expressed in terms of the previous k terms of the sequence,

so its degree is k.

This recurrence includes k initial conditions.

a0 = C0 a1 = C1 … ak = Ck