Question

Consider the nonhomogeneous linear recurrence relationan= 3an−1+ 3n. (a) Show thatan=n3nis a solution of this recurrence relation. (b) Use Theorem 5 to find all solutions to this recurrence relation. (c) Find the solution witha0= 2.

Answer #1

Find the solution of the recurrence relation an =
3an-1 + 5 · 3n

Solve the recurrence relation:
an = 3an−1 − 2an−2 + 3n
with a0 = 1, a1 = 0.

Solve the recurrence relation defined by: an = 3an – 1 + 5 where
a0 = 1
Multiple Choice
an = 7/2⋅ 3n − 5/2
an = 5/2⋅ 3n − 3/2
an = 6 ⋅ 3n
an = 5 ⋅ 3n – 2

Give the general form of a solution to recurrence an
= 2an-1 + 3an-2 + 3n
r^2-2r-3=0
Assume a0
general form: an = c1an-1 +
c2an-2 + · · · + ckan-k
+ f(n) where c1, c2, . . . , ck are real numbers and f(n) is some
function of n.

Find the solution to the recurrence relation an=3an−1+28an−2
with initial terms a0=10 and a1=12.

Find all solutions of the recurrence relation
an=6an-1-9an-2+(n+1)3n

ORIGINAL SOLUTION PLEASE
Find an explicit formula for the following recurrence
relation:
3an+1 - 4an = 0 ; a1 = 5
Write a Python program that tests your result by generating the
first 20 terms in the sequence using both the recursive definition
and your explicit formula

Consider the recurrence relation T(1) = 0, T(n) = 25T(n/5) +
5n.
(a) Use the Master Theorem to find the order of magnitude of
T(n)
(b) Use any of the various tools from class to find a closed-form
formula for T(n), i.e. exactly solve the recurrence.
(c) Verify your solution for n = 5 and n = 25.

find the
solution to an= 3an-1 - 3an-2 + an-3 if a0 = 2, a1 = 2 , and a2
=4

Find a particular solution to the following nonhomogeneous
linear systems"
X' = [ 3 -3 ] X + [4]
[ 2 -2 ] [-1]
First is a 2x2 matrix and second is a 1x2 matrix.

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