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Type I -- Stellar Number


ibworking

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Well you're saying that it equals Sn.

In your first post you said

n 1 2 3 4 5 6 7 8

Sn 1 3 6 10 15 21 28 36

So when n=1, Sn=1. When n=2, Sn=3. So a(22) + b(2) =S2 = 3

Yes? No?

Oh yes i see!! sure .. my head :D

and i could show that with other numbers as well..

so that yould be a good way to prove the equation?

kathy

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That's a good way to find the equation. And you can check several numbers. Are you asked to prove the equation the equation that you found? That is, are you asked to find a general equation and then prove that it works for all numbers? Because the first thing that comes to mind is to use proof by induction, which might not be appropriate, and you might not be asked for it either haha.

If you're just asked to show work for finding the general equation, then just show how you found the coefficients and explain things when you're not sure if you've covered it thoroughly. =)

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That's a good way to find the equation. And you can check several numbers. Are you asked to prove the equation the equation that you found? That is, are you asked to find a general equation and then prove that it works for all numbers? Because the first thing that comes to mind is to use proof by induction, which might not be appropriate, and you might not be asked for it either haha.

If you're just asked to show work for finding the general equation, then just show how you found the coefficients and explain things when you're not sure if you've covered it thoroughly. =)

The question didnt ask us to prove it but i thought if might add to it positively.

It just asks: "Find a gerneral Statement that represents the nth triangular number in terms of n" thats all.

but if i try to get c i would not get 0.

i did: 6=9a+3b+c and if i put 0.5 = a and b then i get for c=-5 but if i do 6=9a-3b+c then i would get c=0 what is my mistake in that? i cant see it, because it makes sense to me like this.

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I'm not sure I understand.

6= 9a + 3b + c

6 = 9(1/2) + 3(1/2) + c = 6 + c

right? 9(1/2) + 3(1/2) = (1/2)(9+3) = (1/2)(12) = 6

I think c=0 works, but once again, you don't want to say c=0, assuming a = b = .5. You want to say a+b+c=S1

4a+2b+c=S2

9a+3b+c=S3

And solve for the coefficients.

Try to find a, b, and c again.

And I don't think that proving it would get you any more points. Ask your teacher and see if he/she gives you an answer. If you really want to prove it, set it aside as the last thing you do, after finishing the rest of the IA. Then go back and add a proof if you have time.

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I'm not sure I understand.

6= 9a + 3b + c

6 = 9(1/2) + 3(1/2) + c = 6 + c

right? 9(1/2) + 3(1/2) = (1/2)(9+3) = (1/2)(12) = 6

I think c=0 works, but once again, you don't want to say c=0, assuming a = b = .5. You want to say a+b+c=S1

4a+2b+c=S2

9a+3b+c=S3

And solve for the coefficients.

Try to find a, b, and c again.

And I don't think that proving it would get you any more points. Ask your teacher and see if he/she gives you an answer. If you really want to prove it, set it aside as the last thing you do, after finishing the rest of the IA. Then go back and add a proof if you have time.

Ohh yes sure sorry i did 9+0.5 sorry :D

yeah i get you why its c=0 then makes sense!!

I wrote it down like this: To prove the equation is right I have to go back to Sn= 0.5n²+0.5n and take out the coefficient which gives us Sn=an²+bn+c.We assume that c=0 which we can after taling in account all of our calculations. If we the substitute numbers in for n=1 or n=2 we get Sn=a*1²+b*1+c = 1 because a and b are both 0.5. Same with S2=a*2²+b*2+c = 3.

does that sound more or less alright? i think that will do it if they dont tell me to show how to prove it or something like that. :D

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I realize this isn't the entire thing, but what you have right now is not in good order.

You should explain why Sn is a second degree polynomial. Why does Sn=an²+bn+c?

Then you need to find a, b, and c. Then you can show that the equation you found works by plugging some numbers in.

Right now you're saying "Here's the answer. Assume ___. [which you need to explain more or take it out]. Plug in numbers and look--it works!" The problem is you can't say that Sn=.5n2 + .5n because when I plug numbers in, it works. How can you say it works for all numbers? So instead, you should do the system of equations thing to find the equation and then go from there.

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Is it possible for me to solve this using more... observational techniques? Would I get a hih grade anyway? I am not brilliant at math but I got a high score on my last portfolio (modelling). If I "notice" patterns rather than find them through mathematical logic does that count? As long as I prove it with mathimatical logic afterwards... Like you know how you just notice a pattern, you look at numbers and you see it... that's what happens for me so if I just explain that process and then back it up with mathematical logic is that still valid?

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Here's my experience with that:

I was working on a different IA [same type, though], and I was doing a logistic function, trying to figure out the different parts of it. I started explaining mathematically. Some of the parts of logistics are straightforward, so that was fine. Then I ended up explaining by subjective manners that lost me points in the math area.

So yes, go with the patterns. But when you do explain the logic, make sure it's truly founded in math, not guess and check. If by logic, you mean what people are talking about in the posts above, then you'll be fine. :)

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Here's my experience with that:

I was working on a different IA [same type, though], and I was doing a logistic function, trying to figure out the different parts of it. I started explaining mathematically. Some of the parts of logistics are straightforward, so that was fine. Then I ended up explaining by subjective manners that lost me points in the math area.

So yes, go with the patterns. But when you do explain the logic, make sure it's truly founded in math, not guess and check. If by logic, you mean what people are talking about in the posts above, then you'll be fine. :)

It was the posts above I guess... I don't really understand it. As I said, I'm not really a math person. Maybe if I work with it a little more then I'll see "the logic"...

I'm just looking at the criteria and it says for a 5 i criteria D for investigation "the student gives a correct justification of the general statement". So I guess that's the only place I would need the types of things in the posts above. Unless guess and check is not a "mathematical strategy". Is it not induction? (or deduction, can never remember the differences) Or could I do mathematical induction as a method to prove my general statement and that would be a mathematical strategy? Because it says I need a mathematical strategy to produce the data. I have multiplied and divided and so on to see the relationships between the term numbers and number of dots, is that a mathematical strategy or just, I don't know, something else?

Thank you :)

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My teacher specifically told me that guess and check wasn't a good enough strategy if I wanted more points. It's not going to get you a zero, but it's not going to get you full, for my teacher. Maybe yours is different.

Mathematical induction is different [and annoying, in my opinion :)].

The reason that guess and check isn't the best strategy is because you can only guess a finite amount of numbers, so you can't say that it'll work for the next number [unless you do mathematical induction... eh]

Your patterning might be sufficient, if as you say there's math involved. I don't know. Because I don't see what you're doing, I recommend trying to find the general equation through the finite differences method as well.

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I need help on this too. What does the part "Hence, produce a general statement, in terms of p and n, that generates the sequence of p-stellar numbers for any value of p at Sn

my first math portfolio is due in three days. we were given the one about the stellar numbers. I am about halfway through, but i am stuck on finding a formula for the stellar numbers. for the 6-stellar number, i found the pattern is you add the previous multiple of 12 to the previous stellar number. but how do you put this in an equation?

example:

table:

1 1

2 13

3 37

to find 37, you go 2(12)+ 13.

The formula I got was -------

ok well i need help with the question......produce the general statement in terms of p and n. no idea what to do there. freakin out because i have about 4 hours left and i haven't figured this out......PANIC ATTACK!!!!!!!!!!NEED HELP PLZ.

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I've never done this IA, but I guess you would find the general statement for specific p values and look for trends.

So when p is 5, 6, 7, etc, what's the general statement in terms of n? And then compare those general statements to get an overarching general statement. I'm not sure if this is right since I haven't done it. I do know that the IA usually leads you toward the right method, so look at what you've been asked to do before this point because it should help you figure this part out.

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I've never done this IA, but I guess you would find the general statement for specific p values and look for trends.

So when p is 5, 6, 7, etc, what's the general statement in terms of n? And then compare those general statements to get an overarching general statement. I'm not sure if this is right since I haven't done it. I do know that the IA usually leads you toward the right method, so look at what you've been asked to do before this point because it should help you figure this part out.

thanks for the gelp. i aprreaciate it dearly, oh and i figured it out :) im so happy. :) my girlfriend doesn't understand though, she sayd im a lamo :/ haha its cool though.

Have you heard of polynomial or quadratic sequences? The way it's been explained to me is you take the terms and find the positive difference between each consecutive term. Then you have a new list of numbers and you find the difference between each terms again, which gives a new list. Then you do the same thing again. You repeat this until you've found a list with all of the same numbers. If you get a list with all of the same numbers, then you know that there's a polynomial that will fit your sequence.

So for example

1, d+1, 2d+1, 3d+1

[take difference]

d, d, d

So that's a first degree polynomial... aka a monomial, which is what you deal with when you say an =a1 + (n-1)d, where d is the difference, because when you simplify, you get an=dn-d+a1

More complicated:

1, d+1, 3d+1, 6d+1

[take diff]

d, 2d, 3d

[take diff]

d, d

Since you've had to take the difference twice, it's a quadratic. If you had to take it thrice, the polynomial would be a cubic. And so on.

Does that help you?

ok so if i have a thrice equation....how is it gonna look like???? what do the variables mean????

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What do you mean by thrice equation?

When you have to take the difference three times? It'll be a cubic. ax3 + bx2 +cx +d

And which variables?

Yeah you have the equation written down. the thing i dont get is how to solve it when i have sequences. like 1 13 37 73 121 181 253

its weird. :/

Edited by Aboo
No text speak!
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heyy

the previous posts have been quite useful to me in doing my portfolio but now i am abot consfused on how to do the general statement in terms of p and n that generates the sequence of p-stellar numbers for any value of p at stage Sn

can someone please expalin me what it means and how can i find it?

thanks alot

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Ok I am doing my IA and it's due in 2 days. I do not understand what it's asking/ what I'm suppose to look for when it says "repeat the steps above for other values of p. Can somebody please help me... please o please.

Edited by sweetnsimple786
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Ok I am doing my IA and it's due in 2 days. I do not understand what it's asking/ what I'm suppose to look for when it says "repeat the steps above for other values of p. Can somebody please help me... please o please.

Don't you do the same thing as you did for the p value that you already found the equation for? Write out the numbers and find the equation that works with it?

What does it mean by the general statement? Is that like an equation? Thank you =)

Yes, I think so.

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