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!
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.
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.
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
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
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?
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.
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.
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
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.
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.
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?
Nice. I remember doing a bunch of problems like this when in elementary school. I also remember the fun of solving problems like this.
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!
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.
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.
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.
got it 4 thanks for the fun.
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.
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
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
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?
Your solution is flawed as the answers provided no not prove out.
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.
@@raynewport9395But if n is chosen from 2,3,4 you get n^2.
You're right. Question is ambiguous.
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.
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
I got it right, but I thought the sequence was that each box had four times the area of the preceding one,. That was an incorrect assumption.
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.
4n?
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.
Did anyone else notice that the prime numbers were written with 1 instead of 2?
D
dsq
n² of course... too simple.
4n
It looks like 2n
My bad n2
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?
What's the 5th term? Rhetorically speaking
4n