Quadratic Sequences - How to find the formula for the n-th term

[@ceriwingkle]

OKAY WHAT THIS WORKED WELL FOR ME AHHHHHHHHHH THANK YOU SO MUCH FOR THIS VIDEO!!!! I spent hours trying to figure this out, but this video helped me a lot!!! Thanks again!

[@RadfordMathematics]

I’m so glad to hear/read it helped :) Thanks for your happy/positive words! The tutorial and notes (with worksheets) on this topic may also help: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html Take care Dani!

[@ceriwingkle]

@@RadfordMathematics Although I have one question if you don't mind asking... I understand when u said that example how 2a= the second difference, 3a+b= The second term minus the first term and so on, But what does a,b and c stand for respectively??

[@RadfordMathematics]

a, b and c are the coefficients you need to find. The generalized formula for a quadratic sequence is u = an^2 + bn + c, all quadratic sequences have a formula like that! The only thing that distinguishes one quadratic sequence from another are its values of a, b and c :) So once you know that you’re dealing with a quadratic sequence you know that it’s formula looks like u = an^2 + bn + c, all you have to do is find its values of a, b and c.

[@tonyserrano9884]

Thank you, it was really clear and i didnt get confused in any part of the whole explanation and whole video, this was a big help.

[@magpiestudent9357]

This really helped me to understand finding the nth term of a quadratic sequence. It is one of the best videos out there on the subject, thank you so much.

[@humidifier8914]

This is 10x easier then the method my teacher taught me, thank you!!

[@lilbakrill7946]

THANK YOU!!! I was pouring over a math problem for hours and feeling so frustrated, then I watched this video, plugged my numbers in, and there it was, so grateful.

[@RadfordMathematics]

Thank you for such a kind message Lilba :) Really glad to hear/read that it helps!!! If you want some extra practice you can see some questions (don’t worry it’s completely free) on my site: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html

[@kalimbwekalimbwe1318]

You are the first person to make me understand after watching so many videos. May you be blessed!!!

[@RadfordMathematics]

Thanks!! I’m really glad it helped 😊

[@mlbb_not_official]

Thanks a lot... Went through many videos but never understood it until I watched your video

[@RadfordMathematics]

Hi Jack, thank you for the kind words, I'm really glad to hear it helped :) If you want you can also practice this topic (with the tutorial) on my site that goes with it. Here's the link: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html Wishing you all the best, John Radford.

[@aishani1591]

I have an exam in like 2 Hrs and I have to go to school and write it! I asked one of my friends to help me out with this particular sequence but he was just as confused as me lol. But I am actually glad that I found this video. Thank you so much for the hard work you put into it and to be honest your doing a great job! You are doing amazing and please keep going. Thank you :)

[@charneschiu]

AWESOME!!!! THANK YOU!!! The best explanation I saw. I spent 3hrs trying to help my son's 7th grade homework. This is such a great video and a relief. Good Karma and Great blessings to you. Subscribed!

[@RadfordMathematics]

Thanks for the kind comment AuAg!!! Truly glad this video helped you and your son 😊 Take good care 🌱

[@abhigyansrivastava4247]

Thank YOU SO MUCH!!!!!!! I WAS SEARCHING FOR AN IDEAL FORMULA FOR THE PAST 6 HRS!!!! Some Videos were fooling me by giving ineffective Formulae!!!! Thanks Genious Ranford

[@RadfordMathematics]

Thanks for your comment 😊 Really glad it helps! Take good care ✌️

[@martha3304]

Thank you, you have explained this in such simple terms, I truly appreciate your help

[@RadfordMathematics]

Thanks for your kind comment 😊 truly glad it helps ✌️

[@dogalraxtheplumber755]

This was such a massive help. Outstanding explanation; thank you!

[@aorm1224]

thank you so much!!! this is easier to understand than most videos I've watched

[@RadfordMathematics]

Thanks Aorm! I’m really glad it helped 😊

[@MohammedAkram-ib2my]

Amazing explanation. Thank you so much John.

[@iankim6236]

This Video helped me so much !! Thank YOUU

[@RadfordMathematics]

+Leute Heute I’m really glad it helped :) Working on adding quite a few new tutorial and webpages these days, don’t hesitate to follow RadfordMathematics.com on Facebook to stay posted :) See you soon!

[@RadfordMathematics]

+Leute Heute you can also check out plenty of practice of quadratic sequences on our site (remember we’re still in the process of adding all the pages...) www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html

[@farhanbatada3272]

This helped a lot mate, thank you

[@msryamayomide2046]

Thank you so much Mr. Radford this really helped me and i know i understand this for good.

[@RadfordMathematics]

Thanks for taking the time to comment, I really appreciate it!! Truly glad it helped Msryam 😊. Take good care ✌️

[@rajkishorenemchand8929]

Very well explained. Easy to understand.

[@RadfordMathematics]

Thanks for your comment! I’m really glad this video helped 😊

[@hidayataiman134]

Thank you so much Mr.radford mathematics!!!!!111This video has helped me with my O levels😂😂😂

[@RadfordMathematics]

Thanks for your message Yoshikage :) I’m really glad to hear/read it helped 😁 If ever you want practice exercises... you’ll find some on my site. Here’s the page on quadratic sequences : www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html Hope it helps 😁 Take care!

[@buhlebenkosingcobo2556]

This saved my life

[@TDgrwm]

u def explained wayyy better than my maths teahcer

[@RadfordMathematics]

Thanks for taking the time to comment Toba! And thanks for your kind words 😊 Maybe your teacher was just having a bad day... happens to all of us at times 😊 Truly glad this helped! Wishing you all the best! Take good care ✌️

[@creamcroissant8137]

You're a lifesaver!

[@D4RK-n4n]

Thank you for making it easier.

[@RadfordMathematics]

Thanks for your comment! I’m really glad it helped 😊

[@Science-TRICKS4991]

Man thank you so much... I owe you indeed

[@basmaalshafay7062]

thank you thank you thank you!!!! , the clearest and simplest video I saw for quadratic equation as i was extremely struggling with it and your video helped me alot, you are a great teacher and i am very very happy that i knew about your channel

[@RadfordMathematics]

Hi Basma! Thank you for such kind words!!! :) I am very glad the tutorial helped! If you want some extra practice, on quadratic sequences, don’t hesitate to visit the page on my site that goes with this tutorial. The link: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html Again thank you for the message! Wishing you all the best, John Radford.

[@zoeturner3258]

This is so helpful!! Thank you so so so much!!

[@aryanmehrotra1162]

this videos is life saver

[@RadfordMathematics]

Really glad it helped Aryan! Thanks for the comment 😊

[@sajalmughal3693]

Thank you so much... You're a lifesaver. 🥰❤️

[@noorjehan9143]

It helped me a lot in my maths exam

[@RadfordMathematics]

That’s awesome! Thanks for your comment! I’m really glad it helped 😊

[@fiddlesticks6146]

AMAZING EXPLANATION!!! TYSM!!!

[@RadfordMathematics]

I'm really glad to hear/read it helped :) Should you need it you can also find this tutorial alongside practice exercises and their solutions on my site: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html (it's still being built... But it's getting there :) ) Wishing you all the very best! John Radford.

[@chahaksrivastava8881]

great video, very helpful!!!

[@RadfordMathematics]

Thanks for your comment Chahak! Really glad this video helped 😊 Take good care ✌️

[@markdavis9990]

That formula is so straightforward

[@maikrorg7171]

YOU ARE GODLIKE, THANK YOU!

[@freshmusic4316]

Ohhh thanks man.you had help in wonder way.again thank you for your service.

[@rixongilefortunateyingwane3861]

You are best of the best🥰🥰🥰

Super Clear and helpful. Thanks

[@RadfordMathematics]

Thanks Clement! Really glad it helped ✌️

[@petermartinovic6887]

You saved me 🙏 thank you

[@RadfordMathematics]

Hi Peter! I'm really glad to hear it helped :) if you want some more practice with notes, tutorials and exercises on this topic check out my site: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html Hope it helps :)

[@RutzBikazy]

Thank u so muchhhhhhhhhhhh....I was struggling😪🥰🥰🤭

[@smrpkrl]

why 2a= second difference a+b+c= first term and so on? please explain on this

[@manjorisarkar7524]

Thanks so much for this video, I’m glad your video’s the first one I found. I just have one question; how did we come up with the 3 equations that you provided us? Thank you so much!! Good luck to everyone revising!

[@কিউব2স্কয়ার3]

I have the same question. Did you get the answer after these 4 months?

[@stephencullen4337]

There is another way to do it with simultaneous equations I think and that’s how we know this

[@samdalal1590]

finally i understand, thx a lot

[@RadfordMathematics]

Hi Sam! I’m so glad it helped :) If ever you want some practice questions, I’ve added some to my site: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html Maybe it could help even more :) All the best, John Radford

[@DcEditorr]

Sir i thank you so much for this because i cant understande my maths sir because is english is little weak thank you sir

[@mxhamedxx]

This is so helpful thank you so much

[@karymefatimacrisologo3208]

omg thank you so much!!!!😭💖

[@alejandrofeliciano2076]

Does this work when the second difference is negative?

[@RadfordMathematics]

Hello Alejandro! Yes it certainly does :) If it helps, you can see some practice questions (with answer keys) here: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html Wishing you all the best, John Radford.

[@jacobjermy3596]

Thanks, this helped a lot

[@AS-zt3dj]

Does no one else listening to this guy with epic Minecraft soundtracks on is well... EPIC!!

[@saeitoshi7201]

I have a question Are there any tutorials on why there is an specific formula for this. I'm talking about the "red" 3:40 edit: or atleast give me what are they called (formulas)

[@lazylei1797]

it his own formula I guess

[@subasishbehera8645]

Awesome videos! Now what if the differences have a geometric sequence i.e. the difference between each terms is multiplied a constant value. It would be a great help.

[@davidhill8163]

a great help thanks

[@RadfordMathematics]

Really glad it helps :) Sorry initially tapped the « thumbs down » by mistake :) If you’d like to practice even more, you’ll find my online notes/exercises on this topic here: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html Hope that helps :) All the best, John Radford.

[@mrkeyzzz]

I'm curious. Do you know how these equations are derived?

[@pierretam2037]

Me too

[@Spiky_Liz4rd]

THANK. YOU. SO. MUCH

[@RadfordMathematics]

Really glad it helped 😊

[@Moved0925]

THANK YOU. SO MUCH.

[@RadfordMathematics]

Thanks for your comment! Truly glad this video helped 😊

[@Moved0925]

@@RadfordMathematics Yes it did!! I used to have 6 mistakes in my tests learning this, now I only have 1 ever since I watch your video! You are so cool! Sending warm prayers

[@sawdustwoodchips]

Good explanation, but would have been good to show how the three equations were derived.

[@RadfordMathematics]

Thanks for your comment! 😊 And I agree! I’m working on making a good video on explaining the “difference method” and the derivation of the various formula it leads to… . Take care ✌️

[@jootpepet]

Is there a shortcht to this? I noticed that C is always equal to the 0th term. Much like in arithmetic sequence

[@joshuasuelan1945]

does this method applicable for higher differences?

[@RadfordMathematics]

Hi Joshua, good question! The answer is « yes » the difference method works for higher powers (such as cubic, quartic, quintic sequences...). In fact you’ll find the link to the difference method for cubic sequences right here: Cubic Sequences - How to find the formula for the n-th term kzbin.info/www/bejne/nXq3YYyOhJaLfLs Hope that helps :)

[@julianm_arquez]

Love from india !

[@mahomedkhamissa9088]

Well explained

[@juanleighkerryepasion5737]

where the number 3 in the equation. " 3a + b = U² - U¹ " came from?

[@NtsimbiKwanele]

How do you find the value of N if you have the value of Tn?

[@mimikiwi5]

wow thank you so much

[@RadfordMathematics]

really glad it helped 😄

[@williamerasmus1891]

thankyou so much!!!!

[@emmanuelfrancis3142]

thank u so much

[@RadfordMathematics]

Thanks Emmanuel 😊 Really glad this video helped! Take good care 🌱

[@kitkat9764]

Thank youuuu!!!!

[@RadfordMathematics]

Thanks for your comment 😊 I’m truly glad this video helped!! Take good care ✌️

[@MarciaArleneDebra]

It is a very good video. All the other use trial and error, and I am not a fan of trial and error.

[@jelmayguardiario8166]

how about this sequence Sir, 0,10,24,56,112,190?

[@anthonypurcell3646]

Thanks!

[@atyahoodotcome1846]

How about square sequence

[@clarizeesmeralda3765]

muntik na umonte yung ads hahah

[@mobgamerz7397]

I have general formula for sum of nth term of quadratic sequence

[@janieyakz6846]

pls what if the sequence is 2, 9, 28, 65, 126,217

[@janahgincolporal5772]

But what if the sequence has square root?

[@Ahwobebwgggyeiiejrbvbtbg3]

Thank u so much u

[@RC-hv2zd]

this didn’t work for me 😔 i tested it with the first two terms, but it didn’t work after that, and i followed all the steps

[@JCKing-yf6dr]

Why didn't my teacher tell me about this😭😭😭

[@RadfordMathematics]

Thanks for your comment JC King! I’m sure your teacher meant well with another method 😊. Wishing you all the best! John Radford

[@ins4rt_username18]

You did a small but important mistake, u0 is the first value of the sequence and not u1. :)

[@RadfordMathematics]

Thanks for taking the time to write your comment Ins4rt_Username (not a simple name to type there) 😊 I truly appreciate it. In fact you can choose to start at u_0 or u_1. It doesn’t actually matter provided you make a choice. In many countries (such as France) sequences always start with u_0 as they are (by default) defined as functions within the set of Natural numbers {0,1,2,...}. In others though sequences are more often defined over the set if positive integers {1,2,3,...}, which is what you came across in this tutorial. Again, thanks for taking the time to comment, I truly do appreciate it 😊 Take good care ✌️

[@ins4rt_username18]

@@RadfordMathematics I did not know that the start of sequences are can vary by country, I thought this would be the same everywhere :D Anyways, thank you for letting me know and take care too!

[@MrNobody86188]

math is 🗿