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