Triangular Numbers 1, 3, 6, 10, 15 Non-Linear Pattern Rules

[@Mr_Becu1]

Without wasting time ⌚wow nice explanation

[@denekadesta8828]

U helped me alot❤good job sir

[@SUBJECTISOLDMOVEON]

admire your talking very clearly writing and multiple uses of your presentation as well specially certain numbers. everyone is different on how they write them. i like how you apply different angles through the process of it on each one. there’s particular set of numbers i’ve seen over 20 years keeps reoccurring shows random daily weeks but shown in many different ways in my life routines. i seen it at the end of your video. i appreciate you thanks..

[@NeverEvi]

Wasn't aware that adding consecutive triangular numbers made perfect squares! Awesome to learn and thank you for making this video!

[@laioconnor8046]

My teacher was explaining it I can't even understand you taught me in just 5 minutes thank you so much

[@snehalkulkarni9975]

Thanks uncle...

[@manishmishra7265]

Sir it was great it helped me for my exam

[@courierdubois]

It took me a while to figure out n(n+1)/2, so I thought I would share my explanation. Basically... the first triangle has one dot on the bottom. The second triangle has two dots on the bottom. The third three. Etc. So we know that the Nth triangle (whatever number in the sequence) will have that number of dots on the bottom. So triangle 132 will have 132 dots on the bottom. The sequence will be 1+2+3 ... 130 + 131 + 132. In other words, the sequence goes 1 + 2 + 3 .... (n-2) + (n-1) + n. In order to quickly add everything together, the most efficient way would be to take the first and last row of dots and add them, then the 2nd row and 2nd last row of dots, and so on. So for triangle number 132, the first dot can be added to 132 dots (the top and bottom of the triangle), which would give us 133 dots. The next set would be 2+131 = 133. The third set 3+130=133. The fourth 4+129=133. Notice how each set of rows we had equal to the same number: 133? Now the question is... how many sets of 133 would you create? Exactly HALF of 132, which would bring you all the way to the middle of the triangle from both ends, allowing you to count ALL of the dots. That's where n/2 comes from. It's just a quicker way then adding 133 sixty-six times. Take the number of dots on the bottom of the triangle, half that number, and that's the number of times you need to add n+1. We know, that if we have... for example... triangle number 546, that we'll be adding 547 exactly 273 times. Or, 547 times 273. I found an explanation of the explicit rule lacking in this tutorial. It needs to be explained more fully. Obviously, we know the pattern isn't a linear one -- but HOW did we derive the equation for this growing pattern? Hopefully this will help. :)

[@ishikameher1941]

This is sooooo helpful! thank you so much. I was kinda' struggling with is topic.

[@kmt7061]

Omg thank you sooo much. I'm doing math online during this terrible pandemic and it's awful 😖 so this is really helpful thanks again

[@khalidmushtaq6367]

I really thanks you sir for understanding this concept.

[@HotlistAnime]

You did all your best to make this video I appreciate it.😁 THX!!

[@parkij11]

All of them & More & Many More.

[@katharinedimoski3069]

Helped me alot. Thanks u explained it the best!!! THX😁

[@pauletduck2590]

This is so helpful, but I don't understand why you divided by 2 in the explicit formula?

[@diannekevubaldo1287]

Wow! u perfectly explained this,thank u so much!

[@SecTechie]

You're a most excellent instructor.

[@HotlistAnime]

not really there is others don't make them fell bad.😇😇👍🏻😁if you want it is how you think it is.

[@coolnoyt2806]

Thanks for doing my homework

[@nshavochauke5955]

Thank u so much, u have no idea how much this has really really helped me

[@MathematicsTutor]

Thanks a lot for appreciation. You are an inspiration Also explore: kzbin.info/www/bejne/iabKn5SwbbqrnbM All the Best!

[@savitakaushik7565]

0

[@LearnWithHasanSir]

👍👍👍👍👍Superb Sir Mera Channel hai Basic maths solve k liye Learn with Hasan Sir aur mujhe aapki ye writing tricks bahot achhi lagi plz aap behind the scene aap kaise shoot kartye ho bataye plzz

[@olivelbb3404]

Thank you so much, this really helped!

[@glmc7200]

Thank you, appreciate it.😁

[@capitalm417]

Hello Sir. Can you please make a video about finding oblong numbers. Thanks

[@rajinair2546]

Thank you so much for making the concept very clear by explaining it so well👍

[@MathematicsTutor]

Thanks. Here are interesting set of formations: Tetrahedron: kzbin.info/www/bejne/iabKn5SwbbqrnbM Pentagonal Numbers: kzbin.info/www/bejne/hIKvgGVmq5mDa7M

[@toma3447]

Just saved my life… :)

[@SoapSeason]

fr bro 😂

[@x_rayquaza3486]

I needed so much help thank you this explanation was so easy to understand

[@ChinmayGawde]

Nicely explained

[@govindarajulu1228]

Thank you sir. Very nice explained

[@revapawar3516]

Thank you sir.you make it easy to understand triangular numbers

[@vijayalaxmit676]

Thank you sir

[@shaghilasubhash6853]

This is brilliant.

[@gmpitts16]

Your explanation of the explicit rule was extremely helpful! Thank you very much!

[@MonikaSharma-pg6ss]

Thank you sir you helped me a lot

[@xshitizchahal6177]

Very very nice explaination

[@mubeench4665]

Thank u sir

[@suvarnavispute7288]

Plz can you post a video on finding bases with given triangular numbers suppose number 15 is giveb and we havr to find its base

[@محمدمحمدالمراكبي]

Thanks this is the best method

[@monaeminter1376]

can u do one on hexagonal numbers ?

[@rovi7670]

It's really good

[@bushangadai579]

Thanks you so much this really help ed

[@neetujha5173]

if you find that the video is blureing for 2 , 3sec at the first than you are like me😒😒 but I understand it.. 😁😁

[@kewenwong54]

So what is the answer for new pattern ? Thanks for response

[@kavidukavidu1413]

Wow 😍

[@parkij11]

Numbers Are Infinite.

[@namanindiamathematics5709]

Very useful

[@leZickzack]

For those who are interested in a Python solution: c=0 erg = 0 add = 1 number = number youre looking for while c < number: erg+= add add+= 1 c+= 1 print(erg)

[@funloversmn6444]

Thank u so much great work

[@jpwyang]

thank you!!

[@monaeminter1376]

how can you make an equation out this problem and is it a function?

[@user-jc2mu8yj5r]

Good, it was very helpful

[@MathematicsTutor]

Thanks a lot for appreciation

[@reyveramino421]

HELLO, SIR, HOW ARE YOU, BEST TEACHER EVER AND SMOOTH😍🥰 WHAT IS THE N-term of this 0,1,2338889, I am actually confused, which one the first term? and what the next term as each number increases, need help asap!🙏

[@Ernie1482]

How do you know to divide by 2 in the explicit rule?

[@MathematicsTutor]

First, we know that the example is not simple as we do not have common difference. The pattern is increasing by different numbers each time. In such cases you need to apply some strategies. This is one of them. With few examples you will learn how and when to apply these strategies. Thanks

[@courierdubois]

It took me a while to figure out n(n+1)/2. Basically... the first triangle has one dot on the bottom. The second triangle has two dots on the bottom. The third three. Etc. So we know that the Nth triangle (whatever number in the sequence) will have that number of dots on the bottom. So triangle 132 will have 132 dots on the bottom. The sequence will be 1+2+3 ... 130 + 131 + 132. In other words, the sequence goes 1 + 2 + 3 .... (n-2) + (n-1) + n. In order to quickly add everything together, the most efficient way would be to take the first and last row of dots and add them, then the 2nd row and 2nd last row of dots, and so on. So for triangle number 132, the first dot can be added to 132 dots (the top and bottom of the triangle), which would give us 133 dots. The next set would be 2+131 = 133. The third set 3+130=133. The fourth 4+129=133. Notice how each set of rows we had equal to the same number: 133? Now the question is... how many sets of 133 would you create? Exactly HALF of 132, which would bring you all the way to the middle of the triangle from both ends, allowing you to count ALL of the dots. That's where n/2 comes from. It's just a quicker way then adding 133 sixty-six times. Take the number of dots on the bottom of the triangle, half that number, and that's the number of times you need to add n+1. We know, that if we have... for example... triangle number 546, that we'll be adding 547 exactly 273 times. Or, 547 times 273. I found an explanation of the explicit rule lacking in this tutorial. It needs to be explained more fully. Obviously, we know the pattern isn't a linear one -- but HOW did we derive the equation for this growing pattern? Hopefully this will help. :)

[@adavallykarthikeya4952]

Mr. anil is that a quadratic sequence so will we be able to deal with it using the an2+bn+c formula

[@gardenofehlesunnah5550]

sir can you make a video on how to locate the inverse of a function on a graph. thanks.

[@MathematicsTutor]

Thanks. Will surely do one for you. Here is one which may also help. kzbin.info/www/bejne/qnLFqKGDZbqseq8 Playlist for Inverse Function: kzbin.info/aero/PLJ-ma5dJyAqpUjOD8bfPL49AiGoag1w8t Thanks

[@abdullahal-shimri3091]

Different topic - triangular numbers make the best spaced-repetition intervals. 1 3 6 10 15 etc.

[@stopitflop]

Thank you so much 💛

[@parkij11]

Alright......... Well Done, Hg Officɑl. How About Steps.

[@tbnr_turtle4445]

Sir could you fix yr camera focus plz

[@MathematicsTutor]

Yes, I am working on it. This video is about a year old. Now I am able to get slightly better results. Need to update the gear. Appreciate your concern. Thank

[@UKgamer978]

How 1dot form triangle

[@rlou9265]

It was helpful.

[@MathematicsTutor]

Great. Thanks a lot for sharing. All the Best!

[@lokeshperumalla16]

Triangle formation Formula No of base dots × no of dots in altitude 1 × 1 = 1 3 × 1 = 3 3 × 2 = 6 5 × 2 = 10 5 × 3 = 15 7 × 3 = 21 9 × 4 = 32 9 × 5 = 45 11 × 5 = 55 11 × 6 = 66 13 × 6 = 78 13 × 7 = 91 15 × 7 = 105 ..... Or Triangle formation 1 = 1 1 + 2 = 3 1 + 2 + 3 = 6....

[@julfiqerjewel9642]

বীজগাণিতিক রাশি

[@parkij11]

All of them & More.

[@parkij11]

& MANY MORE & MANY & EVEN MORE & ALL AROUND THE WORLD AND THROUGH THE YEARS.

[@parkij11]

And Those & These.

[@rubydevi252]

Thanks a lot sir but it's better if you speak in hindi

[@parkij11]

All of them.

[@meetusharma4717]

Sir Will this be inclusive in geometry?

[@sam-um5yt]

Hello Anil

[@k.r.t.vallinone3732]

3, 6, 10, 15........nवां पद what?

[@starinsky2873]

sir is this related to geometry or something like that

[@MathematicsTutor]

It is an interesting pattern and is well know as triangular numbers as it show that number of things that can be arranged in any triangle. Thanks

[@balajienglishmediumschool6835]

Sir why did we take 101 why can't we take 102 or any other no.

[@sherenefate8103]

Why divide by 2?

[@urmilakumari4093]

👍👍👍👍👍👍👍👍👍👍👍👍👍👍👍

[@shalinikumari3011]

Impressive video

[@MathematicsTutor]

Thanks for appreciation. Here is combination with other interesting patterns: kzbin.info/www/bejne/hIKvgGVmq5mDa7M

[@lindsaymunro7791]

My cat heard your voice and became obsessed with my computer. She was looking for you. It was amazing. I watched the video several times because she loved it.

[@MathematicsTutor]

Very interesting. Many birds and animals come near me when I go for a walk. So, it is not surprising. Watch some of my nature videos: kzbin.info/www/bejne/l3S9e5Wvr81shZI kzbin.info/www/bejne/oV6tlmqZnZJqbpo

[@Shah_73]

Sir how many multiple of 5 in this pATTERN till 5000

[@manthanhaldar8759]

Sir what if we have a pattern of 4*4 cross matrix and the pattern is 1 2 4 7 3 5 8 11 6 9 12 14 10 13 15 16

[@ananyaseema252]

Excellent sir thank u

[@dineshgamerz1890]

55

[@aadilmalik9409]

The dot pattern of 1 is not triangular in form or shape

[@eulyzaplayz5931]

Every Triangular Numbers Are Numberblocks Step Squads

[@creepyc_1728]

Wooo

[@parkij11]

All of the Smells.

[@Exphub295]

👌😷😷

[@Exphub295]

Hi

[@Exphub295]

👌👌

[@parkij11]

All Smells & More & Many More & Many & Even More.

[@parkij11]

All Smells & More.

[@parkij11]

All of the Smells Around The World,.

[@parkij11]

& All Smells.

[@achieverstrainingcenter7926]

but isnt it recursive rule not explicit?

[@MathematicsTutor]

In recursive rule we define terms with respect to the previous term. So it is not a recursive rule. Recursive rule will be: t1 = 1, tn = t(n-1) x n Hope that helps. Thanks

[@achieverstrainingcenter7926]

Many thanks for the reply! The teacher told my son that the explicit has to have a common difference, which caused the confusion.

[@MathematicsTutor]

@@achieverstrainingcenter7926 Please Note, Teacher is also correct. We use common difference to get the Explicit Rule if the pattern is Linear. In this example the pattern is non-Linear. Teacher must have provided examples like shown in the link: kzbin.info/www/bejne/pn2tdnZsrLBnqtE Please also watch some more videos in this playlist for which I have given you the link to understand all the related concepts. Feel free to ask questions. Thanks and all the Best!

[@MathematicsTutor]

@@achieverstrainingcenter7926 IMPORTANT: Here is a New Video for your child. Please share to get the concept of common difference and Explicit Rule: kzbin.info/www/bejne/eWaraJ-vd7-bhrc Thanks

[@achieverstrainingcenter7926]

@@MathematicsTutor Oh, thanks for the clarification. Can't thank you enough!

[@parkij11]

Alright.........

[@parkij11]

All Smells.

[@parkij11]

& More Smells.

[@parkij11]

All of these Smells & More.

[@abdelsid1575]

helped me by a million in minecraft

[@MathematicsTutor]

Thanks a lot for appreciation. All the Best!

[@anandakumarpalitpalit9111]

😆😆😆😆😆😆😆😆😆

[@zaraspebongjr.g8937]

Annoying blah blah

[@siddharthnamdeo6967]

too much old fashion way of speaking

[@MathematicsTutor]

ReMix

[@DivyaSharma-qo2em]

viodeo very very poor. Because you do speak in hindi

[@parkij11]

All Smells.