I have a few questions - the ones that usually appear on the third column...
1) How do you add the 1st n triangular numbers?
2) How do you find the difference between like the 3rd pentagonal number and the 3rd haxagonal number?
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Polygonal numbers
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Polygonal numbers
by 101dalmatians » Sun Oct 21, 2012 3:19 pm
I guess this signature really doesn't matter now that I know that the forum is going down soon...
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Re: Polygonal numbers
by darksaber21 » Sun Oct 21, 2012 6:49 pm
The formula to find the sum of the first n triangular numbers is:
[unparseable or potentially dangerous latex formula]
So first five numbers should equal 35, right? Well, the formula works out that way:
[unparseable or potentially dangerous latex formula]
As for the other question, I'm going to show you how it is derived for you. Since the nth number is the same (three in this case), we can do this:
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
So, we got the formula, now to plug in.
[unparseable or potentially dangerous latex formula]
So the answer is three.
Proof: the third pentagonal number is 12, where as the third hexagonal number is 15. The difference between them is 3.
By the way, that formula works for any two shapes where one shape has one more side than the other, and the nth number being looked for is the same.
In case you don't know, just derive it on the fly.
[unparseable or potentially dangerous latex formula]
So first five numbers should equal 35, right? Well, the formula works out that way:
[unparseable or potentially dangerous latex formula]
As for the other question, I'm going to show you how it is derived for you. Since the nth number is the same (three in this case), we can do this:
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
So, we got the formula, now to plug in.
[unparseable or potentially dangerous latex formula]
So the answer is three.
Proof: the third pentagonal number is 12, where as the third hexagonal number is 15. The difference between them is 3.
By the way, that formula works for any two shapes where one shape has one more side than the other, and the nth number being looked for is the same.
In case you don't know, just derive it on the fly.
Now I know the stakes, and I'm willing to show what I gots. I will see you all at state for the first and final time, so let's end the year with a bang! :)
MTHS - Class 5A, District VII, Region I
MTHS - Class 5A, District VII, Region I
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Re: Polygonal numbers
by 101dalmatians » Sun Oct 21, 2012 7:32 pm
That's awesome...Now I can get like 18 more pts on my test....
I guess this signature really doesn't matter now that I know that the forum is going down soon...
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101dalmatians - Ubiquitous Spammer
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