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

[@vanessavisagie9112]

Thank you soooooo much...this really helped😊😊

[@RadfordMathematics]

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 :)

[@AnilChaukekar]

Thanks sir you have helped my son for his final examination.Keep on making such tutorials

[@RadfordMathematics]

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.

[@AnilChaukekar]

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

[@hamsandwich4243]

Really good formula presented in a really easy to understand way. You’re even better than Mr Hegarty!

[@RadfordMathematics]

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

[@hussainok3382]

you can also use the formula: a + (n-1)(p) + (1/2)(n-1)(n-2)(q) + (n-1)(n-2)(n-3) where a = first term in the first level (e.g in this video it was 4) n = term number p = difference in the first 2 terms of the first level (e.g in this video it was 14 - 4 = 10) q = difference in the first 2 terms of the second level (e.g in this video it was 26 - 10 = 16)

[@obsidiansiriusblackheart]

Do you have links to any resources explaining how the 4 cubic equations were derived originally? I'm interested in learning the fundamentals of mathematics

[@udanthalokuliyanage9530]

Thank you very very much. You don’t know how helpful it was. Thank you again

[@RadfordMathematics]

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

[@joshushushu]

thank you so much! your math videos helps a ton! this channel is so underrated. I also use your website! :)

[@RadfordMathematics]

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 😊

[@chiomaalexia4878]

Thank you soo much for all your videos, I just watched the one on quadratics nth tern and it helped a lot, watching this one too😁

[@RadfordMathematics]

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

[@hiyaanjalivenkatesh1803]

That was such a short yet crispy way of learning a very crucial concept! Thanks a lot:)

[@AotearoaAviation]

thanks, my homework is due tmrw and this is a literal lifesaver

[@spacemanthing5204]

but how do you get 12a and 2b from the second diffrence or is it always like this

[@RadfordMathematics]

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

[@amayzingmarta]

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 kzbin.info/www/bejne/jHbNnXutqLSJrqs

[@amayzingmarta]

Im sure you will find it there

[@serahaleyabastin]

but how was the 4 equation made? can u explain to me that ?

[@ghiacencelli45]

I literally had to look at 4 other videos that didn’t explain a damn thing before finding this. Thank you

[@paradox_i-guess3450]

eve of my half yearlys and i pull myslef together lazily and find this video this video might just have helped me score so much better for my exams kind souls like yours help mine and i thank you for that, yours faithfully, random teen :)

[@xdgaming952]

thank you so much! i checked everywhere and got to know this was the better one

[@hanahdilshad6563]

tysm, this really helped me so much. you r a true legend!

[@cristina21restar]

Sir where did you get the equation for differences??

[@chiomaalexia4878]

What if the 3rd difference isn't 6 , but like 2 , would you do 2/6

[@RadfordMathematics]

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

[@cristina21restar]

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

[@mxhamedxx]

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

[@haanirajani7568]

you are a living legend

[@anujinsukhbat4031]

Do you have video where you explain how to get 7a+3b+c or that 3 equations or how can i know 4th power sequence or 5th poqer sequence etc i need to know deep is it something to do with pascals triangle?

[@allisonevin7484]

THANK YOU. this was an amazing tutorial thank you so much.

[@Ali-gh7rj]

What are the rules of a quartic sequence and how would I work out the rules?

[@adil2174]

Ace Inferno an^2+bn+c

[@adil2174]

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

[@Faith-zp5kf]

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

[@Fishc4ke_YuXiang]

Does the formula 6a=6 and so on work on every single cubic equation? Please reply

[@CosmicFever]

its 6a = 3rd difference, not just 6

[@JowellaTrance]

Good am/pm, I have a question. Is it possible to use this equation with an alternating third difference? For example, instead of +6, +6, +6 We have +6, -6, +6, -6 and so on

[@abebuenodemesquita8111]

8:20 not even specifically nonzero. you will end up getting a=0 and then solve you will get a quadratic.

[@mohammedhafiz3137]

Well explained. Thank you so much.

[@Jjfds.Vcfghxssdbfrtgdx]

Nice explanation and thank you so much

[@RadfordMathematics]

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 :)

[@Jjfds.Vcfghxssdbfrtgdx]

@@RadfordMathematics thank you so much

[@jelmayguardiario8166]

what if 4th difference what equation should I use?

[@farhanbatada3272]

This helped a lot mate, thank you

[@RadfordMathematics]

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

[@farhanbatada3272]

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

[@RadfordMathematics]

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 :)

[@farhanbatada3272]

@@RadfordMathematics sure. Thanks man.

[@RadfordMathematics]

Break a leg :)

[@Fishc4ke_YuXiang]

What does Un mean

[@RadfordMathematics]

@@Fishc4ke_YuXiang it refers to the general term of an arithmetic sequence. So for the 3rd term (for example) you’d replace the n by 3 to make it U3, for the 5th term it would be U5… for a generic term we say Un (the n-th term). Hope that helps 😊

[@katlegotalane2476]

Your great at teaching 😭🙏 thank so much

[@AdefunkeMatiluko]

How was the formulas proved?

[@saamqri2507]

massive help, thank you so much

[@RadfordMathematics]

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

[@pardonmypiano3063]

THIS IS AMAZING I WILL NOW ACE MY MATH TEST WOOHOOO!!!!

[@raahimhadi4905]

how did you do

[@MidQo]

*no response*

[@mahirjusvibin]

i cant really solve this sequnce it came on my igcse any help would be apprecaited find the nth term of this sequence 4.75,10.5,16,21

[@LunaLov3good]

Is this IGCSE or A level?

[@RadfordMathematics]

Hi Luna, that would be IGCSE level 😊

[@pierretam2037]

May I ask you? How can we get the four equations? I can understand 1st and 4th equations but I do not know what 2nd and 3rd equations is. Thanks for your explanation.

[@mediwise2474]

Pl expplain

[@kimnguyen1371]

What do u plug in N?

[@Jjfds.Vcfghxssdbfrtgdx]

@kim Nguyen It is just number of term

[@mauve6222]

a bit late but what if i only have 2 differences? meaning after 2 sequences or whatever you call it, the differences remain the same number?

[@nebthegamerartist6662]

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…

[@mauve6222]

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

[@nebthegamerartist6662]

@@mauve6222 alright, no problem!

[@johnli8967]

Sir can i ask whats "u" mean

[@boluwatifedosunmu6858]

those are the terms so u1 is the first term

[@mikhailadal5583]

THANK YOU so much🙌🏻

[@RadfordMathematics]

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

[@alifsofarr]

Thank you so much ❤️❤️❤️❤️❤️

[@squ1dosh995]

My Question is how did you got 2b = 0?

[@rekhabhasin9494]

Please give the formula to find biquadratic progression

[@pardonmypiano3063]

THIS IS AMAZING

[@RadfordMathematics]

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!

[@muhdhuzaifah7628]

Thank you !

[@jeannedenissemendoza4915]

where did the 12a+2b come from T_T, I'm sorry I suck in Math. because its not working with my terms :(

[@A_canofbeans]

I’m just as confused 😍

[@nidhimenon2912]

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

[@sedra5195]

God bless you. this was very helpfulll

[@RadfordMathematics]

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

[@mmh7534]

I am having trouble with the formula for a what i wrote down is 6a=8 and what came out is 1.33 and the sequence is 3, 5, 15, 41,____.

[@madihakhan2677]

Thats great sir thanks

[@pragnajoshi3424]

V good explanation

[@mlgdabgodlim8783]

Bro this saved me from a failing math

[@RadfordMathematics]

That’s awesome! Glad it helped 😊

[@budhansingh8322]

Thanks a lot❤

[@aadityaharikrishnan9970]

soo good!

[@aleksanderprzegalinski7104]

Lovely job

[@harshdhedhi8887]

thanks G

[@saurabhkaushik9629]

Thanks

[@MYSTICHAWKGAMING]

thankyou

[@ryanghuneim3356]

hello ooooooooooooooooooohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh yeeeeeeeeeeeaaaaaaaaaaaaaaaaaahhhhhhhhhhhhhh yyyyyyyyyyeeeeeeeeeeeeeeeeaaaaaaaaaaaaaaaahhhhhhhhhhhh

[@RadfordMathematics]

Undeniable enthusiasm! I like it 😂

[@aishathshero2755]

23 minutes and we are gonna do mock lolll

[@redbox7569]

What is sum formula 😅

[@AbhijitBhattacharyaju]

Can’t believe instead of teaching why he is doing whatever he is doing he is just telling class to start with 4 equations. Really poor way to teach math. It’s like teaching trick and not math He should have talked about 1) why it’s always cubicle if 3rd difference is constant( This comes from differentiation and we can extend it to nth power) 2) why the co-efficients are coming the way it’s coming! (it comes from integration) Now the differentiation and Integration I mentioned are not in continuous domain but in discrete domain. You can go through “difference equations” to understand calculus in discrete domain.

[@wobfog9619]

No I eat chicken