This is the best video on quadratic sequences. All videos from others were so confusing. I finally understand after ages of confusion and frustration. Thanks 🙏
Thank you so much, I didn’t really understood when my teacher thought this at school for 40 min. She used quite hard techniques but thank you so much for teaching this method. Now, I’m being able to finish these kinds of questions faster than the other students and thought them too. Thanks a lot
thanks beast mode maths you really are a beast at mathematics for getting me to understand something. i am now your number 1 fan. i will stay subscribed until i die and i will leave you something in my will for teaching me the nth term. i love you. please don't leave me. stay with me through my igcse's so i can become a beast at maths just like you. love u bro.
You're welcome, Roise. I'm pleased to hear that you now understand how to calculate the nth term of quadratic sequences - they can be tricky! Good luck with your iGCSEs and I'm sure you will also soon morph into a beast.
OMG thank you sooo sooo much! My teacher did not expliain this nearly as well as you! OMG it's amazing and makes so much sense now! Now I can actually do these questions in an exam without thinking I will get them wrong! This is by far the best explaination I have seen!
Thank you for explaining step by step. Often times steps are left out because it is assumed that we understand and know the steps that are unsaid and left out. There was one step that drove me crazy and kept me search for an answer until I got to you. Thank you so much. BTW, I was trying to figure out how to get the _n2(squared #'s) to subtract from the original sequence to final determine the nth term. Thanks again!! (I commented on the wrong video, this comment for this video)
Yes - it doesn't matter what the 2nd difference is. We always divide it by 2 to get the coefficient on the n^2 term. E.g. if the 2nd difference between terms is 3.6, then the sequence would start with 1.8n^2.
At 4:40 timestamp I got kind of confused. Are the small differences just a coincidence, or should my answer always be -1 only? I'm currently following your way of solving it and mine certainly had a huge gap. Thank you by the way!
Hello there. I think I understand what you're asking. So the differences between our sequence and the 2n^2 sequence for each term are 1, 1, 1, 1, 1. This will not always be the case. I go through many more examples in my (part 2 of 2) video which have differences which are different for each term. I hope that makes sense! Thanks 🙂
As you mentioned we half the second difference number to put in front of n square. What if the difference is 1, how do you show that? Please help. Thankyou
@@BeastModeMaths Thankyou so much. I was under the impression that the number cannot be in decimals. This clarifies my misunderstanding. Thanks again 😊
Thanks for this video I have a face to face exam tomorrow even through I had online classes the whole year it is not fair but thanks for the video it helped me allot again I hope I pass
when finding the nth term of the sequence and when you subtract the 2n squared from the sequence, what do you write when the answer to subtracting is different for each number?
Hi Maddy. I have another video dedicated to this, called "More calculating the nth term of quadratic sequences". However, I have gone through an example below on how to do this. 5, 13, 25, 41, 61 The 2nd difference is 4, so we start with 2n^2 s 5, 13, 25, 41, 61 2n^2 2, 8, 18, 32, 50 s-2n^2 3, 5, 7, 9, 11 Now we just calculate the nth term of this arithmetic sequence that is left over (s-2n^2). The nth term of this arithmetic sequence is 2n+1, so we just need to add this on to our quadratic part. Therefore, the overall nth term is 2n^2 + 2n + 1. I hope this helps, but I would recommend watching the video I mentioned at the start.
Hi L. Thanks for watching. Once you have found the nth term of the quadratic sequence, you can just substitute n=50 into your formula. For example, let's say that your quadratic sequence had the nth term of 2n^2 + 4n - 5. You would just replace "n" with 50. Therefore, the nth term would be... 2 x (50)^2 + 4(50) - 5 2 x 2500 + 200 - 5 5000 + 195 5195 I hope that makes sense 🙂
Hello! Great video, but I'm confused as to why in the second quadratic sequence, the squared is placed at the top and not the bottom like the first. Ex, 1,10,25,46,73...I thought those numbers would be below the original sequence and then subtract.
Hi Christina, Thanks for your message. The very first example I went through was a linear sequence (not a quadratic). For all quadratic sequences, we subtract the quadratic part away from our original sequence to see what is left over. So for example, with our original sequence of 1, 10, 25, 46, 73, ..., the quadratic part is 3n^2. We then write down the numbers in the 3n^2 sequence (3, 12, 27, 48, 75, ...) and then take this away from our original sequence to see what is left over. I hope that makes sense!
Hello Jejdiwbcjs Wie2ndoqjwjd, If the second difference is not constant, we just work out the nth term of those numbers. If you watch part 2 of this video series, it specifically goes through these types of examples. For example, if the second difference is +7, +9, +11, +13, +15, then the nth term of this sequence will be 2n+5... so we just add this onto the quadratic part. I hope this helps, but please watch part 2.
A great video! I have a question I am struggling with and I was wondering if you or someone could help. I was asked to write out theses sequences up to the nth term: n squared and 2n-1. How would you do this? Thanks! This video was so helpful.
Thanks for this video So I got a sequence Here: 3, 3/2, 3/4, 3/8 I tried the method in this video but it didn't really resolve after I checked the second differences, that is, it still had varying differences after the second difference. How can one attempt such sequence please?
Hi Patrick, The reason why this method won't work is because this is not a quadratic sequence - this is a geometric sequence, which requires a different method to calculate the nth term. I have a video on this topic. The link is below... ruclips.net/video/f9L_AnEIBas/видео.html I hope this helps! - Let me know if you still need some guidance.
Hi Abdulaziz, We always half the 2nd difference, even if it an odd number. So we take half of 3, which is 1.5. Therefore, the first part of our sequence will start with 1.5n^2. We then do the same steps as before. Write out the 1.5n^2 sequence and then compare it with our sequence to see what is left over. I hope that helped!
Hi Elvi, I have written below my workings out in calculating this. However, I would firstly recommend my part 2 to this topic if you haven't already watched it. You firstly need to calculate the 2nd difference between terms. Ist difference: +7, +13, +19, +25 2nd difference: +6, +6, +6 We then half this 2nd difference. Half of 6 is 3, so our nth term starts off with 3n^2. Now we need to subtract the 3n^2 sequence away from our original sequence to see what is left... Our sequence: 2, 9, 22, 41, 66 3n^2 sequence: 3, 12, 27, 48, 75 If we subtract, we are now left with: -1, -3, -5, -7, -9 We then need to determine the nth term of this sequence and add it on. This sequence goes down by 2 each time so it must start with -2n. Then to go from -2n to this sequence, we have to add on 1 (-2 x 1 = -2, then +1 = -1). Therefore, the nth term of this part is -2n + 1. Overall, if we put the quadratic and linear parts together, we get 3n^2 - 2n + 1. I hope that helped!
Hello. Those numbers (3, 6, 9, 12, 15, ...) are the numbers in the 3 x table. The numbers in the sequence (5, 8, 11, 14, 17, ...) are the same as the 3 x table, but each number has just been shifted up by 2. Basically what I have done is just compared my sequence with the numbers in the 3 x table. I hope that helps.
Hello. The next term in this sequence cannot be found because we don't have enoug h information. It is not an arithmetic sequence because the first difference between terms is not the same (+11, +23, +41). It is also not a quadratic sequence because the 2nd difference is not the same (+12, +19). Now we cannot verify whether this is a cubic sequence or not because for the 3rd difference, we only have one value (+7), and so we have nothing to compare it to. This means that there could be multiple solutions to this problem. You need to be given the 5th term of the sequence, and then you would be able to calculate the 6th term. There may be some online sequence calculators that give you an answer, but these would not be unique solutions. I hope that helps!
Hi Hanan. Unfortunately, I can't help with this (or your other question), as I only teach up to GCSE level. Have you tried searching for this on Khan Academy?
Hi there. Thanks for the comment. This method does work every time. If you wanted to provide me with a quadratic sequence where you think it doesn't work , then I can go through it step by step.
@@theroon1278 So the 1st difference between each term is +9, +13, +17, +17 The 2nd difference between each term is +4, +4, +4, +4. Therefore, the quadratic part of our nth term is 2n^2 (I got the '2' because we half the 2nd difference). Now we subtract the 2n^2 away from our original sequence to see what is left over. Original sequence: 6, 15, 28, 45, 66 2n^2 sequence: 2, 8, 18, 32, 50 Difference: 4, 7, 10, 13, 16. Now if we take a look at the sequence that we have left over, hopefully you can see that this is a linear sequence. We just need to calculate the nth term of this sequence. It is the same as our 3 x table, but each number is 1 more than the 3 x table. Therefore, the nth term of this sequence is 3n + 1. If we combine the quadratic part with the linear part, we get 2n^2 + 3n + 1. I would encourage you to watch part 2 of this topic, where I specifically go through more examples of these types of sequences. I hope that made sense! Best wishes
Hi Adis, What in particular would you like help on? If you're asking about the nth term of this sequence, it looks like when n=even then the term is 3 and when n=odd the term is 17.
thank you so much, first one that made sense
Thanks Caveman! I'm pleased that you found it helpful!
I have been through countless videos on this subject and this by far consists of the best explanation. thank you!!
Hi Stxrraiza,
Thanks for the comment and you are very welcome! I'm pleased that the video helped in your understanding of this topic! 🙂
After that much of time i finally understood... the concept u delivered was perfect ....helped alot..
Thank you, kindly. Very much appreciated!
This was really helpful and well explained, finally I understood it. Keep going
Thanks Raghad. Glad you enjoyed it! :)
This is the best video on quadratic sequences. All videos from others were so confusing. I finally understand after ages of confusion and frustration. Thanks 🙏
Hi Anna. You are very welcome. I'm really glad that you have finally understood! woop woop!!
Im reviewing for my exam and this video helped me thanks
Hi 6PAX. Thanks for the comment and I'm really pleased that it helped!
Thank you so much, I didn’t really understood when my teacher thought this at school for 40 min. She used quite hard techniques but thank you so much for teaching this method. Now, I’m being able to finish these kinds of questions faster than the other students and thought them too. Thanks a lot
You're very welcome, RollerCoaster_111. This can be a tricky topic to understand, so well done! I'm thrilled to hear that you haave grasped this 🙂
Very good explanation. This is the only video in the RUclips that I could understand very well. Thank you
Thanks! Appreciate the comment.
Thank you very helpful and not confusing at all like other RUclips videos more of this type of vids plz ☺️
Hi Suhayla. You're welcome. I'm glad you found it useful.
The best explanation by far.
Thanks Lyno Lee. I'm pleased you found it useful 😀
literally u defined it so well i am a fan of urs
Thank you so much. I'm pleased that you liked it :)
This is explained in simple terms and is easy understand. Thank you!
Thank you very much, Amanda. I'm glad you found it useful.
Great video it is helpful. Thanks for trying to help us
Thanks, Paulette. I'm pleased you found it useful.
Very good teaching, I was struggling with that topic at school, this really helped
Hi Great_Western 2020. Thanks for the comment and I'm pleased this video helped!
Omg you just reached me what My teacher could not I think I will do alright in my test today thanks
You're welcome Toga simp. I hope your test went well today!
Nice one now I know and believe it will help me in my upcoming exams
You're welcome. I hope the exams go well for you!
thanks beast mode maths you really are a beast at mathematics for getting me to understand something. i am now your number 1 fan. i will stay subscribed until i die and i will leave you something in my will for teaching me the nth term. i love you. please don't leave me. stay with me through my igcse's so i can become a beast at maths just like you. love u bro.
You're welcome, Roise. I'm pleased to hear that you now understand how to calculate the nth term of quadratic sequences - they can be tricky! Good luck with your iGCSEs and I'm sure you will also soon morph into a beast.
This video was great 👍 . I finally understood . Highly appreciate it.
Yasaman, you're welcome. I'm pleased it has helped! :)
Thank you , you are the first person that explained it so well I actually understood it!
Thank you very much for your comment. It's really appreciated and I'm glad you found it helpful :)
Yeaaa
Finally! Very well explained thank you!
You're welcome and I'm pleased it has helped. Thanks for the comment 👍😀
thank you it made sense when you explained it
Thanks. You're welcome 😀
Thank you sir 💞. Love from India🇮🇳.
You're welcome Aditya. I hope it helps! 🙂
thank you this is the only video that helped me understand 🙏
You're very welcome Ad4n. 🙂
This was amazing understood it very well.....
Thank you very much, Eiman Ali Khan!
OMG thank you sooo sooo much! My teacher did not expliain this nearly as well as you! OMG it's amazing and makes so much sense now! Now I can actually do these questions in an exam without thinking I will get them wrong! This is by far the best explaination I have seen!
Wow. That's Viriginia! That's lovely to hear that you have understood this topic and are more confident now with answering exam questions 💪
great explanation - i think this is my favourite method :)
Thank you Georgia. 😊
This fully verified my understanding, thank you so much!!
Hi Ace. You are very welcome. Thank you for watching 😀
I did not know. Now I know. Thank you, sir.
You're very welcome, Taül Guedí
Thank you so much 😊
Finally I understood it 😃
Keep teaching!
That's awesome! Pleased to have been able to help out! Cheers 😊
I'm new to your channel.
I'm going to appear for IGCSE exams next month
I can see many videos related to my subject thank you so much
That's great! Best of luck for your exams. I've got some GCSE walkthroughs which you might find useful, for some past paper practice.
THIS WAS SO HELPFUL THANK U SO MUCH
Hi Naomi. You're very welcome :)
Because of you I was able to pass my exam. Thank you so much.
Hi Vulxh. Thank you so much. That means an awful lot. However, it is all down to your hard work and dedication. Well done on passing your exam! 😁
Sir thanks a lot.. your trick is absolutely correct.. And it's working so sir ready for my exam today.
Hey. You're very welcome. Pleased to hear that the video helped. Best of luck with your exam today! 🤞
Very much grateful. Love from Bangladesh
You're very welcome Md.Shamim Hossen!
@@BeastModeMaths My pleasure....
Thank you for explaining step by step. Often times steps are left out because it is assumed that we understand and know the steps that are unsaid and left out. There was one step that drove me crazy and kept me search for an answer until I got to you. Thank you so much. BTW, I was trying to figure out how to get the _n2(squared #'s) to subtract from the original sequence to final determine the nth term. Thanks again!! (I commented on the wrong video, this comment for this video)
You're welcome L.LeMond. I know how tricky this particular topic can be so I tried to go slowly and include all of the steps. Thanks for the comment 🙂
😢😢😢😢😢Thank you so much !!I really appreciate it,I needed this for a month 😂
You're welcome! Pleased to hear you found it useful. 🙂
You explained it so well!
Thanks TL HA :-)
that was really helpful I understand it now, thank you !
You're welcome Sarah. I'm pleased it has helped!
That was really useful thank u sooooo muchh 💛
Thank you for the comment! Really appreciated!!
this helped so much thanks!!
Thanks midnighteddy. Appreciate the comment and I'm glad it helped!
Love this
Thank you!
Wooo this gonna get me through my mocks
Best of luck with the mocks, Max 🙂
Amazing vid, now I understand ⭐️
Thanks SUGA WHITE. 😊
Thank you for this great lesson
You're most welcome. I'm pleased to hear that you enjoyed the video! 🙂
This helped so much! Thank you+
You're welcome, AJ Hype. I'm delighted to hear that it helped!
I'm writting my paper 1 on Thursday and i didn't understand patterns but i understand know thanks for the help Mr
No worries. I hope your exam goes well on Thursday!
What if the 2nd sequence is an odd number? Do you divide it by 2 as well?
Yes - it doesn't matter what the 2nd difference is. We always divide it by 2 to get the coefficient on the n^2 term. E.g. if the 2nd difference between terms is 3.6, then the sequence would start with 1.8n^2.
At 4:40 timestamp I got kind of confused. Are the small differences just a coincidence, or should my answer always be -1 only? I'm currently following your way of solving it and mine certainly had a huge gap. Thank you by the way!
Hello there. I think I understand what you're asking. So the differences between our sequence and the 2n^2 sequence for each term are 1, 1, 1, 1, 1. This will not always be the case. I go through many more examples in my (part 2 of 2) video which have differences which are different for each term.
I hope that makes sense!
Thanks 🙂
@@BeastModeMaths Thank you very much! I'm so glad I found your channel 😭
@@Saavedsss No worries!
As you mentioned we half the second difference number to put in front of n square. What if the difference is 1, how do you show that? Please help. Thankyou
Hi Smiti. If the second difference is 1, then the coefficient on the x squared term will just be 0.5 (half of 1). I hope that helps.
@@BeastModeMaths Thankyou so much. I was under the impression that the number cannot be in decimals. This clarifies my misunderstanding. Thanks again 😊
@@deepsmriti You're welcome. Thanks.
Very nice teaching sir 👍
Thank you!
Thanks for this video I have a face to face exam tomorrow even through I had online classes the whole year it is not fair but thanks for the video it helped me allot again I hope I pass
I'm glad the video helped you and good luck with your exam tomorrow!
@@BeastModeMaths thanks
when finding the nth term of the sequence and when you subtract the 2n squared from the sequence, what do you write when the answer to subtracting is different for each number?
Hi Maddy. I have another video dedicated to this, called "More calculating the nth term of quadratic sequences". However, I have gone through an example below on how to do this.
5, 13, 25, 41, 61
The 2nd difference is 4, so we start with 2n^2
s 5, 13, 25, 41, 61
2n^2 2, 8, 18, 32, 50
s-2n^2 3, 5, 7, 9, 11
Now we just calculate the nth term of this arithmetic sequence that is left over (s-2n^2).
The nth term of this arithmetic sequence is 2n+1, so we just need to add this on to our quadratic part.
Therefore, the overall nth term is 2n^2 + 2n + 1.
I hope this helps, but I would recommend watching the video I mentioned at the start.
Very well explained
Thanks Karen 😊
this was helpful
Pleased to hear that you found it helpful 👍
Can i have a question? What grade does this teach? Is it high? Or college
Hi KC Ortega. This topic is taught in high school in England. It is a higher level topic for pupils around age 14-16.
I wanted to ask: is there a video that explains why half we the second difference, when the formula for the sequence is defined?
Oh never mind, i found the video :)
@@sebinaalla4581 Great! :)
Gracias
De nada 🙂
This was so helpful! How would I fine the 50th term of a quadratic sequence?
Hi L. Thanks for watching. Once you have found the nth term of the quadratic sequence, you can just substitute n=50 into your formula.
For example, let's say that your quadratic sequence had the nth term of 2n^2 + 4n - 5.
You would just replace "n" with 50. Therefore, the nth term would be...
2 x (50)^2 + 4(50) - 5
2 x 2500 + 200 - 5
5000 + 195
5195
I hope that makes sense 🙂
Thank you very much
You're welcome, Junior!
Thank you 🙏
My pleasure 😁
شكرا جزيلا 🤍
👋
Hello! Great video, but I'm confused as to why in the second quadratic sequence, the squared is placed at the top and not the bottom like the first. Ex, 1,10,25,46,73...I thought those numbers would be below the original sequence and then subtract.
Hi Christina,
Thanks for your message.
The very first example I went through was a linear sequence (not a quadratic). For all quadratic sequences, we subtract the quadratic part away from our original sequence to see what is left over. So for example, with our original sequence of 1, 10, 25, 46, 73, ..., the quadratic part is 3n^2. We then write down the numbers in the 3n^2 sequence (3, 12, 27, 48, 75, ...) and then take this away from our original sequence to see what is left over.
I hope that makes sense!
thank you so much
You're most welcome, Manu alphonse 🙂
The amount of times he said difference
I’m joking, and I found the video useful
hahaha. I have a habit of using the same phrases!
I have a question, at 7:15. What if the red ones (-2) is non constant?
Hello Jejdiwbcjs Wie2ndoqjwjd,
If the second difference is not constant, we just work out the nth term of those numbers. If you watch part 2 of this video series, it specifically goes through these types of examples.
For example, if the second difference is +7, +9, +11, +13, +15, then the nth term of this sequence will be 2n+5... so we just add this onto the quadratic part.
I hope this helps, but please watch part 2.
A great video!
I have a question I am struggling with and I was wondering if you or someone could help.
I was asked to write out theses sequences up to the nth term: n squared and 2n-1. How would you do this? Thanks!
This video was so helpful.
I just realised 2n-1 is a linear sequence! Thank you for the video!
@@dazzyc1383 Hi Dazzy C. Glad you managed to figure it out and thanks very much for watching the video :)
Finally 😊😊😊,.....Thanku you
You're welcome, Cassiopia :-)
Thank you ❣❣❣❣❣❣
You're welcome 😊
Thanks chief
No worries, champ
Thanks for this video
So I got a sequence
Here: 3, 3/2, 3/4, 3/8
I tried the method in this video but it didn't really resolve after I checked the second differences, that is, it still had varying differences after the second difference.
How can one attempt such sequence please?
Hi Patrick,
The reason why this method won't work is because this is not a quadratic sequence - this is a geometric sequence, which requires a different method to calculate the nth term. I have a video on this topic. The link is below...
ruclips.net/video/f9L_AnEIBas/видео.html
I hope this helps! - Let me know if you still need some guidance.
@@BeastModeMaths you're really genius. It helped a lot
@@patrickdominic4325 thanks 🙂
Thanks
You're welcome 😊
Thanks man enjoy the sub 😊
You're welcome, Hassan. Thanks!
If the number on the second diff is 1 do you still half it
Hi Christeleen. Yes you do. If that is the case, then the nth term would start with 0.5n^2.
What if the second difference between each term is +3?
Hi Abdulaziz,
We always half the 2nd difference, even if it an odd number. So we take half of 3, which is 1.5.
Therefore, the first part of our sequence will start with 1.5n^2. We then do the same steps as before. Write out the 1.5n^2 sequence and then compare it with our sequence to see what is left over.
I hope that helped!
Yes I get it now
Great news, Tyler! 🙂
what if its an odd number how should you balf that
It's the same. E.g.if the difference is 7, then the quadratic part would be 3.5n^2.
may i ask? how if the sequence is : 2, 9, 22, 41, 66 . anyone can tell me ?
Hi Elvi,
I have written below my workings out in calculating this. However, I would firstly recommend my part 2 to this topic if you haven't already watched it.
You firstly need to calculate the 2nd difference between terms.
Ist difference: +7, +13, +19, +25
2nd difference: +6, +6, +6
We then half this 2nd difference. Half of 6 is 3, so our nth term starts off with 3n^2.
Now we need to subtract the 3n^2 sequence away from our original sequence to see what is left...
Our sequence: 2, 9, 22, 41, 66
3n^2 sequence: 3, 12, 27, 48, 75
If we subtract, we are now left with: -1, -3, -5, -7, -9
We then need to determine the nth term of this sequence and add it on. This sequence goes down by 2 each time so it must start with -2n. Then to go from -2n to this sequence, we have to add on 1 (-2 x 1 = -2, then +1 = -1). Therefore, the nth term of this part is -2n + 1.
Overall, if we put the quadratic and linear parts together, we get 3n^2 - 2n + 1.
I hope that helped!
but....how did you get those numbers 3 6 9 12 15
Hello.
Those numbers (3, 6, 9, 12, 15, ...) are the numbers in the 3 x table. The numbers in the sequence (5, 8, 11, 14, 17, ...) are the same as the 3 x table, but each number has just been shifted up by 2. Basically what I have done is just compared my sequence with the numbers in the 3 x table.
I hope that helps.
what is the 5th term in the following sequence? 5,16, 39, 80 and please tell me how it will be .... Thanak you
Hello. The next term in this sequence cannot be found because we don't have enoug h information. It is not an arithmetic sequence because the first difference between terms is not the same (+11, +23, +41). It is also not a quadratic sequence because the 2nd difference is not the same (+12, +19). Now we cannot verify whether this is a cubic sequence or not because for the 3rd difference, we only have one value (+7), and so we have nothing to compare it to. This means that there could be multiple solutions to this problem. You need to be given the 5th term of the sequence, and then you would be able to calculate the 6th term. There may be some online sequence calculators that give you an answer, but these would not be unique solutions.
I hope that helps!
DOES THIS FORMULA WORKS NON-SEQUENTIALY MATTER?
This method of calculating the nth term only works for quadratic sequences.
Will you please send me link why we take half of second difference with n2
Hi Suhail,
Here is the video - ruclips.net/video/9cKBB9VE6Sg/видео.html&ab_channel=BeastModeMaths
I hope you find it useful!
@@BeastModeMaths thanks a lot it really helps me.
4:00 how did you get 2? isn't 2(1)² = 4 ?
No - Because of orders of operation, we do the squared operation first and then multiply by 2. Therefore, 1^2 = 1, and then 2 x 1 = 2.
أستاذ كيف يمكنني ايجاد formula لمتتالية متذبذبة oscillate ؟
Hi Hanan. Unfortunately, I can't help with this (or your other question), as I only teach up to GCSE level. Have you tried searching for this on Khan Academy?
Better
Sometimes this method does not work. 2/3 times it does not work as the 2nd sequence you make has a differance at every number
Hi there. Thanks for the comment. This method does work every time. If you wanted to provide me with a quadratic sequence where you think it doesn't work , then I can go through it step by step.
@@BeastModeMaths 6, 15, 28, 45, 66
@@theroon1278 So the 1st difference between each term is +9, +13, +17, +17
The 2nd difference between each term is +4, +4, +4, +4.
Therefore, the quadratic part of our nth term is 2n^2 (I got the '2' because we half the 2nd difference).
Now we subtract the 2n^2 away from our original sequence to see what is left over.
Original sequence: 6, 15, 28, 45, 66
2n^2 sequence: 2, 8, 18, 32, 50
Difference: 4, 7, 10, 13, 16.
Now if we take a look at the sequence that we have left over, hopefully you can see that this is a linear sequence. We just need to calculate the nth term of this sequence. It is the same as our 3 x table, but each number is 1 more than the 3 x table. Therefore, the nth term of this sequence is 3n + 1.
If we combine the quadratic part with the linear part, we get 2n^2 + 3n + 1.
I would encourage you to watch part 2 of this topic, where I specifically go through more examples of these types of sequences.
I hope that made sense!
Best wishes
@@BeastModeMathsWow thank you you so much! Thank you for your quick response
@@theroon1278 You're very welcome 🙂
nth term of 2 3 5 8 12
@mariadeagrella - Hello. Which part would you like help with?
17,3,17,3 is there any one who can help me
Hi Adis,
What in particular would you like help on? If you're asking about the nth term of this sequence, it looks like when n=even then the term is 3 and when n=odd the term is 17.
Why is grade 8 math already so confusing fml
This can be a tricky topic for a lot of people, but you will get there!
@@BeastModeMaths lol thanks,
We wrote our test, it went pretty well thanks to this video 🙃🤝
@@Wtfqayyam I'm glad it went well :)
Thank you very much
You're welcome, Takesure :)
Thanks a lot
You're very welcome, William.
thanks
You're welcome :)