You would have to define 'n' pretty tightly for any of those answers to be correct. Without that all the suggested answers have no substance.
@TJMusicNerd9 ай бұрын
I understand your reasoning, but I think there is an alternate solution as well. Instead of counting the dots, count the segments on the side of the diamond (1,2,3) and you end up with the number of squares (1,4,9) which is d) n squared.
@IMTM17 ай бұрын
I also used the area of the apparent squares as the basis of the sequence. Perhaps our assumption that these were squares was not an absolute given? but all we get is crickets from the host...smh
@krwada9 ай бұрын
Nice. I remember doing a bunch of problems like this when in elementary school. I also remember the fun of solving problems like this.
@raynewport93959 ай бұрын
The areas are 1, 4, 9, so why isn't "d) n squared" a good answer? He says "we can kind of forget the diamond shape". Why can you decide to throw away certain information in the question? I am sure Mr Math Man won't answer, but can someone else explain please?
@genelowry56669 ай бұрын
Your solution is flawed as the answers provided no not prove out.
@raynewport93959 ай бұрын
Can't immediately see the flaw in "n equals the number of units of area in each pattern". A pattern is a specific layout, not merely a bunch of dots that can just be counted. None of the 4 answers suggested seem to "describe the pattern", but at least "n squared" gives a clue to a square arrangement.
@charlesmrader9 ай бұрын
@@raynewport9395But if n is chosen from 2,3,4 you get n^2.
@nosonkopel68583 ай бұрын
You're right. Question is ambiguous.
@thomasharding18382 ай бұрын
The problem is that the "pattern" was not defined. I saw it as the areas being the square of the side so "n" referred to area relation to the side, or n squared.
@H.G.Wells-ishWells-ish9 ай бұрын
I chose [4-squared] incorrectly. But, it has been 30+ years since my last calculus course and completely forgot what sequences were. Thanks for the refresher!
@charlesmrader9 ай бұрын
n^2 would be the right answer is you look at the area of each "diamond" divided by the dot-to-dot distance along the white lines, for n = 2,3,4.
@henkhu1009 ай бұрын
You show that the formule (function) 4n is correct for n=1, 2 and 3 But if you write that the problem is about a sequence, the domain is the set of positive integers the formula has to be true for n=4, 5, 6 etc as well. In your definition the number of elements in a sequence in infinite large, because you say that the domain is the set of of positive integers. So each positive integer gives an element of the sequence. Please proof that the formule is correct for all integers. Example of a proof: For square number n we have n+1 dots on each side. 4 sides give 4(n+1)=4n+4 dots but each corner has been counted twice. So the number of dots is 4n+4-4=4n
@nosonkopel68583 ай бұрын
Only idiots insist their way of looking at something is the RIGHT way. Sequence of dots? Of segments? Of areas? Of height? Of the perimiters? Ambiguous.
@jebbiekanfer88439 ай бұрын
Doing better, I took AP algebra1 and 2, geometry, trigonometry in high school. I took algebra, trig and calculus but was probably pre calculus in college. It’s been a while and I’ve forgotten more than I ever learned. I keep coming back and beating myself up. Lol
@MrMousley9 ай бұрын
I'm going to guess that it's 4n ... with the n changing from 1 to 2 and then to 3 The first one has 4 dots 4 x 1 the second one has 8 dots 4 x 2 and the third one has 12 dots 4 x 3 I could of course be completely wrong as to WHY that's the right answer.
@russelllomando84609 ай бұрын
got it 4 thanks for the fun.
@jebbiekanfer88439 ай бұрын
4n?
@ianwebster22968 ай бұрын
I agree that without a defining the values in the sequence, the diagrams are su ject to interpretation and alternate solutions. If you define the value of each diagram as the number of intersections of dots and rods, then the sequence is 8, 16, 24and the correct answer could arguably be c) 8n.
@sekharb66519 ай бұрын
dsq
@panlomito9 ай бұрын
n² of course... too simple.
@kennethwright8709 ай бұрын
D
@advancetechnologysolutions66349 ай бұрын
4n
@timchapman67029 ай бұрын
It looks like 2n
@timchapman67029 ай бұрын
My bad n2
@jerryclasby96287 ай бұрын
What's the 5th term? Rhetorically speaking
@IMTM17 ай бұрын
Horrible host! This was posted a month ago and you have not responded to any of your viewers/commenters. Last one of your videos I will click on. Too bad, they were fun respites for me. Is this how you treat your students?