Question

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

Answer #1

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

A sequence is defined by a1=2 and an=3an-1+1. Find the sum
a1+a2+⋯+an

Find the solution to the following lhcc recurrence:
??=−2??−1+24??−2 for ?≥2 with initial conditions a0=1,a1=4.
The solution is of the form: a?=?1(?1)^? + ?2(?2)^?
For suitable constants ?1,?2,?1,?2with ?1≤?2. Find these
constants.
r1=
r2=
a1=
a2=

find the
solution to the recurrence relation ak=ak-1+2ak-2+2 with the
initial condition a0=4 and a1 = 12

Let a0 = 1, a1 = 2, a2 = 4, and an = an-1 + an-3 for n>=
3.
Let P(n) denote an an <= 2^n.
Prove that P(n) for n>= 0 using strong induction:
(a) (1 point) Show that P(0), P(1), and P(2) are true, which
completes
the base case.
(b) Inductive Step:
i. (1 point) What is your inductive hypothesis?
ii. (1 point) What are you trying to prove?
iii. (2 points) Complete the proof:

Let a0 = 1, a1 = 2, a2 = 4, and an = an-1 + an-3 for n>=
3.
Let P(n) denote an an <= 2^n.
Prove that P(n) for n>= 0 using strong induction:
(a) (1 point) Show that P(0), P(1), and P(2) are true, which
completes
the base case.
(b) Inductive Step:
i. (1 point) What is your inductive hypothesis?
ii. (1 point) What are you trying to prove?
iii. (2 points) Complete the proof:

solve the non-homogenous recurrence relation for
an =
2an-1+an-2-2an-3+8.3n-3 where
a0 = 2, a1 = 6 ve
a2=13
Find characteric equation by plugging
in an = rn
try to solve general solution and solve nonhomogeneous
particular solution
and find total final answer please..
My book anwer is
A(1)n+B(-1)n+C(2)n+k3n
, A=1/2, B=-1/2, C=1 ve k=1.
can you give me more explain about this please..?

Using the recursion formula an+1 = (3an - 2)^1/2, with a1 = 4/3,
do the following by induction.
a. Show the sequence { an } is monotone increasing.
b. Show the sequence is bounded above by 2.
c. Evaluate the the limit of the sequence.

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

Let a1 = [
7
2
-1
]
a2 =[
-1
2
3
]
a3= [
6
4
9
]
a.)determine whether a1
a2 and a3span
R3
b.) is a3 in the Span {a1,
a2}?

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