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Eelarch · Aug 23, 2009, 05:47 AM

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?

galactus · Aug 23, 2009, 06:06 AM

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.

Eelarch · Aug 23, 2009, 06:43 AM

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

galactus · Aug 23, 2009, 07:02 AM

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 $L=14$