SOLUTION: The sequence u_n is defined recursively by the rules
u_1 = 3, u_2 = 3, u_(n+2) = u_(n+1) + 2u_n for all n ∈ N.
Find the formula for the general term of the sequence and pro
Algebra.Com
Question 1021209: The sequence u_n is defined recursively by the rules
u_1 = 3, u_2 = 3, u_(n+2) = u_(n+1) + 2u_n for all n ∈ N.
Find the formula for the general term of the sequence and prove it.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The characteristic polynomial is 
, which has roots 
. So the general term is of the form ^n)
for some constants a and b.
When n = 1, we have  + b(-1) \Rightarrow 3 = 2a - b)
.
When n = 2, we have  + b(1) \Rightarrow 3 = 4a + b)
Solving for a and b, we get a = 1, b = -1. So the general formula is
^n)
for all 
.
RELATED QUESTIONS
https://artofproblemsolving.com/texer/japjtbbh
Suppose that {{{u_n}}} is a sequence of (answered by ikleyn,math_tutor2020,lotusjayden)
The sequence u_n is defined recursively by the rules
u_1 = 2, u_2 = 4, u_(n+2) =... (answered by robertb)
lim( n->infinity) U( n) for the sequence 1/2, 1/4, 1/6,... (answered by Edwin McCravy)
The sequence is defined recursively. Write the first five terms.
{{{a[1]=-3}}};... (answered by Edwin McCravy)
1. Compute the Fourier transform of the following signals.
2. (a). x(n) = u(n) –... (answered by Fombitz)
How do I determine whether the sequence converge or diverges. If it converges, give the... (answered by Theo)
If a sequence is defined recursively by f(1)= -2 and f(n-1) = 3(n-1)-4, then find the... (answered by ikleyn)
List all elements of the set A ∩ B, where A = {n ∈ N | n = 2^n − 1} and (answered by richard1234)
If U equals the Universal set which is equal to {1,2,3,4} and if X = {2,4}, Y = {2,3,4}... (answered by Fombitz)