Question

Find all solutions of the recurrence relation

a_{n}=6a_{n-1}-9a_{n-2}+(n+1)3^{n}

Answer #1

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

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.

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

2. Given the recurrence relation an = an−1 + n for n ≥ 2 where
a1 = 1, find a explicit formula for an and determine whether the
sequence converges or diverges

Consider below recurrence relation
f_(n )=f_(n-1)+ f_(n-2) for n ≥ 3. f_(1 )=1 and f_2 = 3
(a) Please compute the first seven numbers in this sequence.
(b) Find the closed form for this recurrence relation. Solving
the characteristic equation, and solving for constants

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

Solve the Recurrence Relation T(n) = 2T(n/3) + 2, T(1) = 1

Solve the recurrence relation an =
8an−1 −
16an−2 (n ≥ 2) with the
initial conditions a0 = 3 and a1 = 14. Show all your work.

Solve the following recurrence relation
T(1) = c1
T(n) = 2*T(n/2) + c2

Solve the following recurrence relation, subject to the basis.
S(1) = 2 S(n) =2S(n/2) + 2n

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