2/3, 1, 3/2, ___What is the next number is the pattern? 

The answer could also be (c) 5/2 because the sequence is arithmetic progression according to ... start with 2/3 then add 1/3 then add 1/2 so then add 1/1 - which equals (c) 5/2. The progression is decreasing the denominator -1 each step, so 3, 2, 1. So I maintain two answer are correct - (b) and (c). Both have 'rules' covering progressive steps, but the rules are just defined differently.

I'd also like to add that to go from 2/3 to 1 you add 1/3 and to go from 1 to 3/2 you add 1/2. We observe thta the denominator is decreasing by 1 with each addition, which would make our next addition 1/1. So our fourth term can be expressed as 3/2 + 1/1 = 5/2. I personally believe you cannot explicitly state that there is only one correct answer and the others are wrong. I can find many, many possible solutions for the fourth term in the sequence, it doesnt mean they're wrong however. We're not exactly limited by how many ways we can generate the next term, and this is due to the nature of only being presented with three previous terms.

Since the problem does not define how many numbers there are in the pattern (a finite number or infinite), I think one could theoretically make a case for 5/2 also being correct in at least one case. To get from 2/3 to 1 you add 1/3. To get from 1 to 3/2 you add 1/2. If we look at the pattern of what is being added (1/3, 1/2, ...), the next addition could be 1/1 to complete the pattern (1/3, 1/2, 1/1) where the denominators decrease by one each time. So if you take 3/2 + 1/1, which would actually be 3/2 + 2/2, you get 5/2. Note that 5/2 only works if the pattern ends at the number in question. Otherwise if the pattern has one other number added to it, you would end up adding an undefined number 1/0 to keep the pattern going (1/3, 1/2, 1/1, 1/0) which would break the pattern. So this is a case where the problem to be solved needs to be defined more specifically. For instance there is a difference between the problem presented in the video which was 2/3, 1, 3/2, _? compared to if the problem were presented as 2/3, 1, 3/2, __, ...?

I'm confused. I changed all the numbers into fractions with common denominator. I got 4/6, 6/6, 9/6. So it would add the numerator first by 2 than by 3, so next should be 4. I got 13/6

Numerator - 2, 2.5, 3. Denominator 3, 2.5, 2. So 3.5/1.5 = 7/3 You can always find many patterns in a sequence of 3.

b) 9/4 increase by 50% From the using fractions

9/4, going up by 1.5. 😎. Thanks for re-activating my maths brain after 40 years of neglect.

Starting with 2/3 you would have to multiply by 3/2 to get 1 (well .. 6/6 actually) then if you multiply 1 by 3/2 you get 3/2 (or 6/6 x 3/2 = 18/12 which is 3/2) So the 'link' is x 3/2 each time ... meaning that the next one would be 3/2 x 3/2 = 9/4

Before you gave the correct answer ... I select 9/4. Multiply the first number by 3/2 to get the second number, multiply the second number by 3/2 to get the third number etc.. So, 3/2 x 3/2 = 9/4. A valid answer could also be 1, but that's not one of the choices. Consider every other number to be an inverse of the previous number ... 2/3 becomes 3/2, 1 becomes 1 (its own inverse).

b) 9/4. 1 is 50% than 2/3; 3.2 is 50% more than 1. 3/2 . To get 50% more than 3/2, multiply 3/2 x 3/2. That yields 9/4.

“So to go from 2/3 to 1 mult by 3/4”. Okay, I get the math BUT not the process. The sequence shown has 4 known elements and one unknown. My approach was to convert the one into a fraction-1/1-and (unsuccessfully) work from there. Your solution is to insert a hidden fraction and perform an operation to get to the next value in the sequence. That is not apparent! And that seriously held me up in understanding your lesson. Not the arithmetic, not the operations but the sleight of hand-the process-to re-order the elements in a form that can be “processed” correctly. Now I realize that a lot of algebra IS understanding how to approach numbers and variables, and often how to move them around so you can perform operations upon them. No problem there. But when presented with a sequence is it really “fair” to have a special operation between one pair of elements that isn’t required for the next? I’m asking from the perspective of a student trying to grasp the lesson: this was a complication that added a layer of complexity to solving it, one I think you did not recognize (though you certainly explained it). And of course, thanks for the lessons. For a variety of reasons they are appreciated.

Always Great to know how to do all types of Math

C) 5/2

Carl Linderholm _Mathematics Made Difficult_ "Guess the Next Number" advises always go for minimal polynomial. It's always applicable, it's general. In this case 4/6 6/6 9/6 _ calls for 13/6.

Always Great to know how to do math.

got it 9/4 add 1/3 add 1/2 add 3/4 progressivly increasing worked for the choices provided. kinda stumbled into the correct ans. thanks for the explaination.

I get: 4/6, 5/5, 6/4, so 7/3 is the answer.

These types of questions are poorly posed. If you say it's a geometric sequence, then fine. Each term is the previous multiplied by 3/2. But you have three terms an infinite number of ways to generate them. It could be that you add first 1/3, then 1/2, so the next one should add 1/1, and 5/2 is the answer. Each term could be the product of the terms on either side, so the next one is 3/2. You can always create a rule such that the next term is anything you want it to be.

This is a problem where the answer is limited to the 4 choices. So your really looking for the one that fits best or that you can make some kind of sense out if.

I’ve never heard of sequencing, and I’m terrible and this kind of math problem, but when I looked at this problem, I saw 1 in between 2/3 and 3/2, so I wondered if I could just cross multiply and get the right answer. 2/3 • 3/2. The answer was 9/4, but I doubt that method would hold up when 1 isn’t the middle sequence number or if the either of the other terms don’t equal one. I probably confused everyone.

I say 9/4, because you are adding half the value of the term to get the next term

I got C. 5/2 because the pattern the numbers are going up by is 1/3, 1/2, 1/1. You have to convert 1/1 to 2/2 to add to 3/2, which equals 5/2.😅❤🎉

9/4

okay but 2/3 = .66, 1 = 1 , 3/2 = 1.25 so we are going up .33 then up .25 so next would be .17 as we are taking away .08 every time so the next answer would be 1.42 or 1 21/50

As I do often- you may have noticed- I like to revisit problems to see if I remember what to do to solve them. Obviously I had forgotten the "geometric sequence" and tried to solve this one again by figuring out addition instead of multiplication. Bummer! :( Maybe next time I will think about it.

Answer 5/2. Add a third, then a half, then one.

Professor, I am sure the answer is 5/2, thanks

What would you use this type of equation for.

c) 5/2

- deer’s left antler - right antler - patterns on the deer's left hind leg part

I got the 9/4 for the wrong reason (I just looked at the sizes and 9/4 looked about the right size.) I was almost there because the first thing I was thinking is that 2/3 and 3/2 are reciprocals and multiplied make 1, and you had the sequence 2/3, 1, 3/2. I should have realized the 3/2 is the other side of 1 which means the jump was x 3/2. I'm only recently trying to regain my foundational math skills so I can go on to learn the higher stuff so just getting that far makes me feel a little better about just bodging a guess.

B) 9/4

b) 9/4

7/3

I think it is 9/4 because the number increases by 50% each time.

b or c

5/2

Multiply each term by 3/² to get next term 😊

1/2

4/9

Geometric sequence? Now that's a new one for me. I was stuck with making sense of the gap between the numbers and got nowhere because there was no logic there to speak of. The smoking gun was perfectly hidden in this problem. Good job Mr YT Math. Next time I will look for the geometric sequence if I can't make sense of the logical explanation.

I timed 3x3 then 2x2 😊

2 1/4 9/4 is just another way of putting it.

How to understand this sum 1 1/3 x 2

First sequence of numbers could have been primes also, yes? thus 11 could have also been correct? 'cept i'm silly and 2 would have been there.. lol. my bad :D I did get 9/4 right at least ;)

D1/2

I approximated the correct answer using the differences between the terms. Note: The vid author's method is obviously better, so remember his method--not mine--which is inferior to his. 1 - 2/3 = .333 3/2 - 1 = .5 .5 - .3 = .16666 (which is 1/6) So, ..5 + .1666 = 1/2 + 1/6 = 4/6 = 2/3 So, 3/2 + 2/3 = 9/6 + 4/6 = 13/6 = 2 1/6 So which answer is closest to 13/6 = 2 1/6? 9/4 (2 1/4) (a bit high, but pretty close.) 4/3 (1 1/3) is too low 5/2 (2 1/2) is too high 1/2 is way too low.

= 2 1/6 .

I just multiply 2x2 then 3x3 =9/4

13/6 surely!

B

i stared at it for ages and got nowhere until i mentally expressed the terms as x ⁄6. Then i got it almost instantly. Not sure what that says about me, but hey-ho, at least I got there.

A

I got 9/4 as each number in the sequence is going up by half the value of the previous one. It's kinda like a fibonacci sequence dependent on the previous number.

Why not 3/2 to the power of -1, 0, 1 , 2? Surely neater, non-longwinded. 3/2 squared is 9/4.

This is not math, it is a game with no rules. I have taken lots of math but never used a comma for scientific notation. Waste of time!

Like your stuff. Thx. However, I have to agree about you wasting our time about the importance of “Subscribing”. Anyone who has spent 10 minutes on YT knows that. Please stop disrespecting us. Thx.

Your overly-long emphasis on getting people to subscribe has the reverse effect. It's the reason why I won't subscribe. It may well be the reason I won't watch any other videos from you. I'm looking for the challenge of figuring out a problem , not listening to some long-winded, irrelevant talk not related to or pertainent to the problem.

B)9/4

9/4

5/2

b) 9/4

B

9/4

B) 9/4

5/2

B