# Thread: 2nd-order recurrence sequence (simultaneous equation mind block)

1. ## 2nd-order recurrence sequence (simultaneous equation mind block)

Hi,

I'm trying to find the closed form of a second-order sequence. I'm down to the 'general solution' which is ( Un = A6/5^n + B(-2)^n ), but I'm having a simultaneous equation mind block.

Here's where I'm stuck:

U0 = 2 gives A + B = 2
U1 = 12 gives 6/5A - 2B = 12

Please can someone help to jog my memory on simultaneous equations, I'm staring blankly at these and Mathcad isn't helping.

Thanks.

2. Originally Posted by mezhopking
U0 = 2 gives A + B = 2
U1 = 12 gives 6/5A - 2B = 12

Please can someone help to jog my memory on simultaneous equations....
You can review this lesson, but a quick set-up might be:

. . . . .A + B = 2

. . . . .B = 2 - A

. . . . .(6/5)A - 2(2 - A) = 12

Then solve the linear equation.

3. Thanks for the jog, but I'm now not sure I factored out correctly .

The original equation was:

r^2 + 4/5r - 12/5 = 0; which is (r - 6/5)(r + 2/1)?

Does this look correct to you?

Thanks...

4. Originally Posted by mezhopking
The original equation was:

r^2 + 4/5r - 12/5 = 0; which is (r - 6/5)(r + 2/1)?

Does this look correct to you?
If you're not sure of your factoring, then multiply the factors back out and make sure you get what you'd started with.

(You should; the factorization is correct.)

5. Thanks! I really don't know why I forgot about such a simple test ... Looks like all is correct.

Ta much.