Cubic Sequences - How to find the formula for the n-th term
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- Опубліковано 7 жов 2024
- Cubic Sequences, how to find the formula for the n-th term, using the difference method.
Cubic sequences of numbers are characterized by the fact that the third difference between its terms is constant.
We learn the formula as well as how to use it using 2 examples.
Visit the Cubic Sequences Page on my Website Here:
www.radfordmath...
Thank you soooooo much...this really helped😊😊
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 :)
Thanks sir you have helped my son for his final examination.Keep on making such tutorials
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
Really good formula presented in a really easy to understand way. You’re even better than Mr Hegarty!
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
Thank you very very much. You don’t know how helpful it was. Thank you again
Thanks for your comment Udantha 😊
I’m truly glad this video helped!!!
Take good care ✌️
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)
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😁
Thanks for your comment 😊 so glad to hear / read it helps!!!
That was such a short yet crispy way of learning a very crucial concept! Thanks a lot:)
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 :)
thank you so much! your math videos helps a ton! this channel is so underrated. I also use your website! :)
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 😊
I literally had to look at 4 other videos that didn’t explain a damn thing before finding this. Thank you
thanks, my homework is due tmrw and this is a literal lifesaver
THANK YOU. this was an amazing tutorial thank you so much.
thank you so much! i checked everywhere and got to know this was the better one
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
Well explained. Thank you so much.
tysm, this really helped me so much. you r a true legend!
Nice explanation and thank you so much
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
massive help, 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 ✌️
you are a living legend
Your great at teaching 😭🙏 thank so much
This helped a lot mate, thank you
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 :)
Does the formula 6a=6 and so on work on every single cubic equation? Please reply
but how do you get 12a and 2b from the second diffrence or is it always like this
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 ua-cam.com/video/VEjlHwsOVxI/v-deo.html
Im sure you will find it there
THANK YOU so much🙌🏻
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
soo good!
God bless you. this was very helpfulll
Thanks for your kind comment! It really helps 😊
I’m truly glad this video helped!
Take good care ✌️
THIS IS AMAZING
I WILL NOW ACE MY MATH TEST WOOHOOO!!!!
how did you do
*no response*
but how was the 4 equation made? can u explain to me that
?
THIS IS AMAZING
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!
Thank you so much ❤️❤️❤️❤️❤️
Thats great sir thanks
thanks G
V good explanation
Thanks a lot❤
What if the 3rd difference isn't 6 , but like 2 , would you do 2/6
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
What does Un mean
@@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 😊
What are the rules of a quartic sequence and how would I work out the rules?
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=)
Lovely job
How was the formulas proved?
thankyou
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
Sir where did you get the equation for differences??
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.
Pl expplain
what if 4th difference what equation should I use?
8:20 not even specifically nonzero. you will end up getting a=0 and then solve you will get a quadratic.
Thanks
Is this IGCSE or A level?
Hi Luna, that would be IGCSE level 😊
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,____.
Please give the formula to find biquadratic progression
My Question is how did you got 2b = 0?
hello ooooooooooooooooooohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh yeeeeeeeeeeeaaaaaaaaaaaaaaaaaahhhhhhhhhhhhhh yyyyyyyyyyeeeeeeeeeeeeeeeeaaaaaaaaaaaaaaaahhhhhhhhhhhh
Undeniable enthusiasm! I like it 😂
where did the 12a+2b come from T_T, I'm sorry I suck in Math. because its not working with my terms :(
I’m just as confused 😍
12 a +2b thats the formula. For the 2nd equation
What do u plug in N?
@kim Nguyen
It is just number of term
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
Bro this saved me from a failing math
That’s awesome!
Glad it helped 😊
Sir can i ask whats "u" mean
those are the terms so u1 is the first term
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?
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!
What is sum formula 😅
23 minutes and we are gonna do mock lolll
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.
No I eat chicken
I am pretty sure I did it wrong. Please help! 5,12,18,19,29