Ask Me Help Desk - Reccurance relations

Ask Me Help Desk (https://www.askmehelpdesk.com/forum.php)

- Math & Sciences (https://www.askmehelpdesk.com/forumdisplay.php?f=402)

- - Reccurance relations (https://www.askmehelpdesk.com/showthread.php?t=389591)

reccurance relations

Two sequences are generated by the recurrence relations Un+1=Aun+10 and
Vn+1=2Avn + 6

the sequences approach the same limit as n --> infinity

determine the value of a and evaluate the limit

So far I have got L=6/1-(A/2)

L=8?

Is this what you have?:

$u_{n+1}=Au_{n}+10$

$v_{n+1}=2Av_{n}+6$

If so, since they approach the same limit, we have $L=AL+10$

and $L=2AL+6$

Solve the system?

I do not get 8.

Would you then sue a simultanius equation to get the answer?

L=AL+10
L=2AL+6

A=4?

but if that's so then it wouldn't work because if there's a limit then -1<A<1

If we solve $L=AL+10$ for L, we get $L=\frac{10}{1-A}$

Sub into the second one:

$\frac{10}{1-A}=2A(\frac{10}{1-A})+6$

$A=\frac{2}{7}$

and $L=14$

All times are GMT -7. The time now is 08:28 AM.