If x_{1}=-1,\ x_{2}=1,\ X_{n}=3X_{(n-1)}-|2X_{(n-2)},\ \forall n\geq3. Find the gene

remolatg

remolatg

Answered question

2021-08-22

If x1=1, x2=1, Xn=3X(n1)2X(n2), n3. Find the general term Xn

Answer & Explanation

l1koV

l1koV

Skilled2021-08-23Added 100 answers

Step 1
The given recurrence relation is
xn3xn1+2xn2=0
The characteristic equation is
r23r+2=0(r1)(r2)=0
has the roots r1=1 and r2=2
Step 2
Since the roots are distinct, the general solution is
xn=c1r1n+c2r2n
=c11n+c22n
=c1+c22n
Step 3
Plug the initial conditions to find the value of constants.
1) 1=x1=c1+2c2
Also
2) 1=x2=c1+4c2
Step 4
Solving (1) and (2).
Subtract (1) from (2).
2c2=2c2=1
From (1),
c1=3
Step 5
Thus the general solution becomes
xn=3+2n
which is the general term.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Discrete math

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?