4:54 , it doesn't mean you've gone wrong, it just shows that there isn't a bn , so the equation would be an^2+c. I have come across a question where the answer is a quadratic but is in the form of n^2+c instead of n^2+bn+c
Thank you do much i didnt learned anything at all but dont worry im subscribe and i like you because all your other vedios helped me and you helped makr my teacher proud by me
Got a sequence that involves n^3 and took me 4 difference of sum to get same ones... how would I convert the amount of times it takes to get a common difference to the power that I am looking for?
Maybe you will be able to work out the pattern....just try the simplest sequence of powers of 4: 1, 16, 81, 256, 625, 1296, and what is the 4th difference? Then the pattern should emerge...
@Davey: We have found the first part of the formula is 8n^2, so we can subtract that to leave the rest which will be linear. Looking at a simpler example: 3, 8, 15, 24,...The differences go up in 2's, so we know that the formula starts with n^2, so we subtract 1, 4, 9, 16 respectively to leave 2, 4, 6, 8 and can see that the linear formula for these numbers is 2n. So now we can put the two formulas together to get n^2 + 2n
You could try it yourself: what happens with the simplest example: 1, 4, 9, 16, 25,...What are the second differences? Then try multiplying up by an integer, say 10, so you get 10, 40, 90, 160, 250,...What are the second differences? Can you answer your question?
If you had to find the differences 4 times before they converge, would that mean the answer should be in the form an^4 + bn^3 + cn^2 + dn + e or should it just be an^2 + bn + c? The sequence is 1, 3 ,12, 39, 120, 316, ... which makes the differences 2, 9, 27, 81, 196 and then 7, 18, 54, 115 then 11, 36, 61 then 25, 25 If it should be the first option, do I just repeat the steps again and again or is there another way to do this?
@David: Think about the sequence of square numbers: 1, 4, 9, 16, 25,... The differences are 3, 5, 7, 9,... And the differences between the differences are 2...so we divide by 2 to get the number to multiply n^2
That's harder than this one....it will involve cubing, not just squaring. If you haven't looked at cubic nth term yet, try writing each number in your pattern as a product of two numbers and look at 2 patterns...
I've been struggling with this for a full year! Thanks so much this finally makes sense!
You are so welcome!
Thaaaankkk youuu I was definitely going to fail this test thx for this explanation
@Krishna Pol: Thank you! Hope your test went well!
Thanks I need this for my GCSE
@Blue Buddy: Thank you!
@@MathsWithJay Thanks. I needed this.... not really I'm in Year 8...
Not anymore
@@pawelpow same but your not
Same here..
The explanation was terrific!
Wonderful Job Frau Jay!
My pleasure 😊
this helped me impress my maths teacher ty so much
@navin navin: That's great! Thank you!
This was so confusing to me, you made it so easy to understand, thanks for making this
You're welcome!
helped a lot im doing IGCSE extended maths and this really did help, thank you :)
You're very welcome!
@@MathsWithJay Hello, i wanted to ask, why went finding the an, we needed to divide the 16 by 2. pls and thank you.
Edit: an^2
@@poplil3934 we apparently need to divide by 2 every time
4:54 , it doesn't mean you've gone wrong, it just shows that there isn't a bn , so the equation would be an^2+c. I have come across a question where the answer is a quadratic but is in the form of n^2+c instead of n^2+bn+c
Yes, you're right - that is another possibility
Thank you do much i didnt learned anything at all but dont worry im subscribe and i like you because all your other vedios helped me and you helped makr my teacher proud by me
Do you have a question about this video?
Thank you for sharing your knowledge! Are there similar methods to find higher degree series as well?
Yes, there are.
Got a sequence that involves n^3 and took me 4 difference of sum to get same ones... how would I convert the amount of times it takes to get a common difference to the power that I am looking for?
It should be 3 rows of differences to get n^3
Maths with Jay why do u divide it by 6 when it's 3, and divide by 2 when it's 2? what about n^4 ._.
Maybe you will be able to work out the pattern....just try the simplest sequence of powers of 4: 1, 16, 81, 256, 625, 1296, and what is the 4th difference? Then the pattern should emerge...
Best explanation and step by step working of topic Thanks
You are welcome
@2:32, why do we divide it by 2??
Look at the simplest quadratic sequence, the square numbers: 1, 4, 9, 16, 25,... and work out the second differences....what do you get?
Why is it -8 I am so confused it was positive 8 before
@Davey: We have found the first part of the formula is 8n^2, so we can subtract that to leave the rest which will be linear. Looking at a simpler example: 3, 8, 15, 24,...The differences go up in 2's, so we know that the formula starts with n^2, so we subtract 1, 4, 9, 16 respectively to leave 2, 4, 6, 8 and can see that the linear formula for these numbers is 2n. So now we can put the two formulas together to get n^2 + 2n
@@MathsWithJay i still dont get how this makes it a minus
This is the second time I am watching this vid and it is still helpful
You may like to look at this: ua-cam.com/video/5iLAGcz4Vfk/v-deo.html
what if when you find the an^2 it becomes negative automatically, like -8n^2, Then is it 8n^2?
@Hari: Why would you change the sign from negative to positive?
i mean if that happened then you would have --8n^2 so it would become positive. but im not 100% sure
It doesn’t become minus, the sign was there just to signify that it is being subtracted from the other sequence
awesome your the best math like rananjum
@Anirudh: Thank you!
Thank you, helped me do my homework correctly 🎉
That's great!
Hi, how do i determine which term has the value given to me using the formula?
Solve it as an equation
does it have to be divide by 2 each time? or is that only for this specific quadratic equation?
You could try it yourself: what happens with the simplest example: 1, 4, 9, 16, 25,...What are the second differences? Then try multiplying up by an integer, say 10, so you get 10, 40, 90, 160, 250,...What are the second differences? Can you answer your question?
@@MathsWithJay Thanks! This video really helped me with my school homework.
Best video on the topic!
Wow! Thank you!
Hello I love 💓 you’re explanation Tysm
@Afsana Rahman: You’re welcome 😊
Do we always have divide by 2 or does it change?🤔
Always 2
u slayed fr fr
yw
I don’t get where you got + 2 from
At what time in the video?
This helped me a lot thanks!!!
Glad it helped!
you deserve a LIKE :D
Thanks, Yasser! 😁
watching this one night before igcse maths exam cuz none of my teachers helped... thank you for saving my life 🙏
Good luck!
What if the difference you get (when finding bn+c),is different ?
@Nadir Sajid: What is your sequence?
Why do you do minus 8 instead of positive 8 for 8n^2???
At what time in the video?
Great vid my brudda
@Joe: Thank you!
my brudda
Thank you so much I need this to finish my homework
Glad I could help!
How did it became -3? 5:03
We need to subtract 3 from -1 to get -4. See ua-cam.com/video/vvayGlslby0/v-deo.html
Why do we make it 3n from 8n and how?
At what time in the video?
Great vid. Thx for the help.
@MatZio Addo: Thank you!
Good Job thanks for you kind help and tutorial Keep it Up !😉
Thank you!
Right I’ve done this for like 2 hours on the same question pretty sure I’m doing something stupid what’s the nth term for to 1, 3, 6, 10, 15, 21
This method will work....have you worked out the first stage yet?
I must be unteachable when you put 8n² in the table and got -32 I was like how
8x2x2
Thank you very much Jay
You are very welcome
What if you don't have the first 4 but instead the 2nd 3rd and 5th term only
@Ross: Have you been told what kind of sequence it is? (Linear, quadratic, ...)
@@MathsWithJayit's quadratic but don't worry i managed to solve it but thanks!
I can't understand at the end that is( +2) concept .plss mam reply me
At what time in the video?
@@MathsWithJay at 5:36, i mean c=2 is come from where
-1+3=2 See ua-cam.com/video/vvayGlslby0/v-deo.html
Is there a way to find the nth term of a quadratic sequence without using that formula?
A method that doesn't use a formula?
Like, a way that you can just calculate it without that formula, i learned it that way in high school but i forgot it
If you had to find the differences 4 times before they converge, would that mean the answer should be in the form an^4 + bn^3 + cn^2 + dn + e or should it just be an^2 + bn + c?
The sequence is 1, 3 ,12, 39, 120, 316, ...
which makes the differences 2, 9, 27, 81, 196
and then 7, 18, 54, 115
then 11, 36, 61
then 25, 25
If it should be the first option, do I just repeat the steps again and again or is there another way to do this?
Kieran, it's the first option. You could find the coefficient of n^4 first and so on.
Why was 16 divided by 2?
At what time in the video?
Thank you so much ♥️
You’re welcome 😊
I got -2 and +3 would that also be right?
@Annika: -2 and 3 for what?
What do you do when the differences are not the same? Plz help
Can you give an example?
@@MathsWithJay I think it's known as a cubic sequence
Do the third set of differences come out to be the same as each other?
@@MathsWithJay yes they do
Then start by dividing the common difference by 6, that will give you the coefficient of the cubed term
Thanks a lot!!!
It is really really helping me! God bless you!! 😇😇
@Alhamdulillah: Thank you!
What if 8n squared is negative
@Henry: Squaring would always give a positive number.
@@MathsWithJay thanks really helpful
aa tysm! greatly appreciated :)
Glad it helped!
Thank u so much.
You're most welcome
tomorrow i have maths exam and this topic was left out ....thanks
Most welcome 😊
what if the diffrence of the diffrence is 0
@Hari 0: Which difference? The first or second?
Why do you divide 16 by 2
@David: At what time in the video?
2:36
@David: Think about the sequence of square numbers: 1, 4, 9, 16, 25,... The differences are 3, 5, 7, 9,... And the differences between the differences are 2...so we divide by 2 to get the number to multiply n^2
@@MathsWithJay Oh thanks
im subbing.
Thank you
Interesting
Thank you!
Thank you so mutch
You are welcome
what if the difference is 2
@Geronima: We always divide the difference by 2. So 2/2 = 1.
helpful thanks
welcome!
thank you !
You're welcome!
why n=4?
At what time in the video?
@@MathsWithJay 5:50, i mean, why do we choose 4 of all numbers?
Pls can you help me out with 2,12,36,80.
That's harder than this one....it will involve cubing, not just squaring. If you haven't looked at cubic nth term yet, try writing each number in your pattern as a product of two numbers and look at 2 patterns...
Why is it plus 2
At what time in the video?
5:30
That part is looking at a linear sequence like: ua-cam.com/video/vvayGlslby0/v-deo.html
Thanks
@The Real Bleach: Thank you!
ty bro
welcome!
tysm
You're welcome
❤
😍
My exam is tomorrow 😭
Hope it went well
@@MathsWithJay it did thankfully 😅
same :' )
im vegan btw, very cool!
Does that help you to find the nth term?
Loooll
lol