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

Thanks for the kind words Vanessa! I'm really glad to hear it helped :) Should you wish to you can find practice exercises and worksheets to download on my site (that goes with this tutorial) at the following link: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/quadratic-sequences.html The site is still being built but may still be useful :)

Thank you for your kind words Anil Chaukekar! I am truly glad it helps. Your son can also practice with some solved examples on my website: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/cubic-sequences.html The site is still being built but, as you can see, some of the pages are functional. Wishing you all the very best, John Radford.

www.radfordmathematics.com You deserve it sir he was able to solve all the questions in the exam.Thanks again sir

Thank you for such kind words :) Should you need some extra practice questions on cubic sequences (with answers) and of course the tutorial you can find some on my site (still being made but getting there :) ) See link : www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/cubic-sequences.html

Thanks for your comment 😊 so glad to hear / read it helps!!!

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

Thank you very much for your kind comment 😊!!! I’m truly glad it helped! My website is still « work in progress » but it’s great to hear/read it’s helping as well! Take good care Deidara 😊

Hi :) it is indeed always like that (always 12a + 2b). I am planning on making a tutorial on the derivation as well soon :)

Good job! However, you know if you're given formula that's ok. I wonder how they come from. I saw good explanation about n-th term for quadratic and even cubic sequences by Daniel Dallas (here is a link to this video below my comments). He explains in the easiest way how to calculate coefficients. If you do it will be more clear Math Science by Daniel Dallas ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-VEjlHwsOVxI.html

Im sure you will find it there

Thanks Farhan! I’m really glad it helped :) If you want a few practice questions you’ll find some on my website: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/cubic-sequences.html All the best! John Radford

That was quick.. have my exams tomorrow hope it goes well

I know the feeling :) Hopefully it will help a bit. Make sure you’re comfortable in distinguishing quadratic and cubic and that you know the formula for both. Provided you know those that should hopefully be a good start :)

@@RadfordMathematics sure. Thanks man.

Break a leg :)

Thank you Ali 😀 Really glad to hear/read that it helped!!! If you want/need any extra practice on this topic you’ll find that tutorial and some questions (with solutions) on my site: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/cubic-sequences.html All the best :)

@@RadfordMathematics thank you so much

Thanks for taking the time to comment Saamqri, I really appreciate it (it helps a lot!). Truly glad this video helped 😊 Take good care ✌️

Thank for your comment Mikhaila 🙂 I'm truly glad it helped!! If ever you want some more practice on this topic, you can find some questions (and answers) on my site : www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/cubic-sequences.html

how did you do

*no response*

Thanks for the kind words :) Really glad to see it helps!! If you want you can practice more with the exercises (and free worksheets) on my site. See link here: www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/cubic-sequences.html All the best!

yes 😊 no matter what it is: you divide it by 6. If it helps: the online notes (with practice examples) can be found on my site (still under construction but there are some things there): www.radfordmathematics.com/algebra/sequences-series/difference-method-sequences/cubic-sequences.html

@@RadfordMathematics is there a reason why we always have to divide it by 6?

@@cristina21restar no, its a fixed formula, and it works for all cubic sequences

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

Ace Inferno an^2+bn+c

2a=2nd diff 3a-b=2nd-1st term a+b+c=1st term

@@adil2174 3a+b=2nd term-1st term actually=)

That’s a quadratic sequence, and it is solved differently… Note that the form of quadratics are: an^2 + bn + c You can go about it by finding second difference, and then dividing it by 2. Say my 2nd difference was 4, i half it (or divide by 2), and I get 2, so the first part is 2n^2. Now you want to list the sequence of 2n^2, which is: 2, 8, 18, 32, 50… And then the original sequence: I haven’t listed it since I’m not giving and example Then, subtract to find a difference and a new LINEAR (well hopefully) sequence will form, if not it may be a constant one. If you subtract and all numbers are, let’s say, 2 (so difference is 2, 2, 2, 2, 2…), your sequence is hence 2n^2 + 2… BUT if it’s linear, (say differences are 5, 7, 9, 11, 13) you then have to solve the LINEAR one and then add it on to the previously stated 2n^2 which I have mentioned. If that were to be the difference, the linear solve would be 2n + 3, so final sequence would be 2n^2 + 2n + 3… I hope this helps and also im a middle school student myself so I ain’t that great at explaining…

@@nebthegamerartist6662 thanks so much! i figured out that it was a different sequence (somehow) but this definitely helped a ton!

@@mauve6222 alright, no problem!

Pl expplain

@kim Nguyen It is just number of term

That’s awesome! Glad it helped 😊

those are the terms so u1 is the first term

I’m just as confused 😍

12 a +2b thats the formula. For the 2nd equation

Hi Luna, that would be IGCSE level 😊

Undeniable enthusiasm! I like it 😂