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

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!

@@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??

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.

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.

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

Thanks!! I’m really glad it helped 😊

Thanks for your kind comment 😊 truly glad it helps ✌️

Thanks Aorm! I’m really glad it helped 😊

+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!

+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

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

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

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

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!

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

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

Really glad it helped Aryan! Thanks for the comment 😊

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 ✌️

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.

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

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.

Thanks Clement! Really glad it helped ✌️

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

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 :)

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.

Thanks for your comment! Truly glad this video helped 😊

@@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

Really glad it helped 😊

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.

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

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

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 ✌️

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

Me too

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

really glad it helped 😄

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 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-gIT0YXO1XFY.html Hope that helps :)

it his own formula I guess

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 ✌️

@@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!

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