5

1 V2 Let An A(ker: 1 - <x<6+ neNand A = ( An: Find sup(A). n2 n2+n+5 n=1...

Question

1 V2 Let An A(ker: 1 - <x<6+ neNand A = ( An: Find sup(A). n2 n2+n+5 n=1

1 V2 Let An A(ker: 1 - <x<6+ neNand A = ( An: Find sup(A). n2 n2+n+5 n=1



Answers

21. $$a_{1}=2, a_{2}=1, a_{n+1}=a_{n}-a_{n-1}$$

This question asked us to determine the 1st 6 terms of the sequence. We know a of one is too. Therefore able to is a of one which is two divided by one plus a of one, which gives us 2/3 if three gives us A ve to divide by one. Plus, I have to, which gives us two fest I have three is gonna be a two or eight start A four is going to be using a three's. That's gonna be a three divided by one plus a of three. A of five is gonna be a four divided by one plus a four. You can kind of see the pattern by this point and then lastly, if sex is gonna be a of five, which is 2/9 divide by one plus a five, which is going to give us to over 11.

Yeah, I've never actually been asked this problem before, so uh I'm just gonna work it out. So we're given that the a matrix is one by one, so to figure out a squared uh what you need to do is actually, how about this? I'll rewrite that is eight times A. So what you need to do is take that a matrix 1111 And multiplied by the 1111 Matrix. So as you go to do this, rose by columns, you're going to get the same entries in all of the um places, but it's one times one plus one times one. So that's going to be too, yeah, there's one plus one is two and that's going to be the same for all of the, you know, this role in this column to this row, in this column to this row, in this column. Also to now before getting ahead of yourself for a cubed. What I would do is I would realize that it's a squared times A. So we just figured out that a squared was that to to to to matrix And then the a matrix says I multiply it is 1111. So as I go to do rose by columns now, I mean I get two times one is two plus two times one to get elements of four. So 4444 I don't know if you realize a pattern going on yet. Um because the next one, like if I did eight of the fourth, I would take a cubed times a So it's going to be that 4444 matrix times 1, 1, So as you go to do rose by columns again, it's gonna be four plus four or eight, 888 So the moral of this is uh if you're doing a to the 10th power, I think you can realize that these are going to be powers of two. I don't know if that's obvious to you, But this is like 2 to the zero power. Um This is two to the first, this is two squared, this is two cubed. So it makes sense to me that each entry is two to the N -1 because it was the fourth power here. And this was Um to the 3rd, 2 to the N -1, 2 to the N -1 and 2 to the N -1 for each uh huh element. So that's the answer I would come up with.

This question gives us a formula and asked us to determine the 1st 6 terms of the sequence. So we know that A of oneness one, we know that a of two is gonna be a of one plus one, which is gonna be two. And then a of three, four a of five, where you can see that we're following a pattern. We got 1 57 for a five and then, lastly for a of sex.

So you are the sequence. Determine Great inspiration We start with, they won't be one e the cuisine misstep is before shrug the do you stand there you have. So we're meant to give six points, so Well, the 1st 1 is for free. You have your you won. Now, what is gonna be you too? So using this equation? Well, it is gonna be or this minus one. But a one is one She was gonna be or minus one. That is three you to help. Me too. You can go ahead and do it. Three. So have the firming up. Three is gonna be four my nose. So you have for three people and equals. So a three week before minus two or minus two for minus three one? No, before ableto for my see through you Very three's run. So four for my land buddies. So well, uh, I is that you're gonna see what he's gonna be fly from here. So right, you can see that she legal to one because before minus for you, choose three four minus three. That's equal to one. It is what it seeks. You know, people through because 60 Makoto for minus five, and this one is not or I was once. So these three, indeed, as well. You dozy like, is, uh, some alternate. Easy. Because you goes well, uh, do you before my nose, they used them. But those terms keep repeating we one. So you used to strike for? I want lots of this sequence. He's one one work you can you do better than lived out, but only the Sikhs who stares.


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