Bruh im a new IBDP student and was so scared and confused with mai (i did not know a single thing) but now i can keep up with others so thank you deeply from my heart and wish you the best
-Arithmetic sequence is a linear function Tn=a+(n-1)d Tn=a+dn-d -Sum of an arithmetic sequence is a quadratic function C equals zero An²+bn na+(.5n²-.5n)d The functions intercept at T1=S1 na+(.5n²-.5n)d (0)a+(.5(0)²-.5(0))d=S(0)=zero
THANK YOU I was studying and I could not understand Why they put this worked for the life of me. They did the whole explanation of how Sn =a1 +a2 and putting it the other way around but the way the book put it was super confusing thank you so much it's like a light bulb clicked in my head.
Thank you so much dear Teacher In our university level our Teacher told us to only learn this formula but not told us how to actually drive this😢😢😢😢😮 formula
He is adding the SAME series but in reverse order. ( see around 4.20( This gives a new series which of course has TWICE the value of Sn ... but because one has added terms in reverse order... each term becomes a constant value - and so becomes easy to evaluate. Then to get Sn.. you divide by 2 An easy way to see this is imagine adding the simple series 1,2,3.... to say 10. ( where d =1, and n =10) If we reverse the series and add it to each original term... we get: 10+1, 9+2, 8+3,.... 1+10. You can easily see that this is now simply adding the constant term of 11 ten times = 110, and to get Sn we divide by 2 = 55. Now its easy to adapt the same idea for other series with other values of difference between terms and number of terms etc as shown.
I’m trying to understand how do you know that taking the first three terms is enough to derive the formula, why not the first two? Why not just the first?
If I want to write a sub n in terms of a sub 1 wouldn’t that be a1 + (n-1)d? I’m just trying to understand how you changed all the other terms in terms of the first term but not a sub n
this is why the education system is wrong... and props to organic chemistry teacher for explaining why and how the formula was made that interconnects with the answers
Because we r considering the term from backwards, like Suppose the term is 5, 8, 11, 14 So if we consider the sequence in increasing order, is that, we wanna find the *last term* , then it will go on like this 👉 5 + 3 , 8 + 3, 11 + 3 = 8, 11, 14 But if we consider the sequence from backwards , is that, we have to find the *first term* by reversing the order (for understanding) : let's say , the sequence now goes like this 👉 14, 11, 8 , 5 ; but note that the sequence still remains in it's orginal form, i.e., (5, 8, 11, 14) as you can see, the sequence now goes like this 👉 14 - 3, 11 - 3, 8 - 3 I mean, if we reverse the order for understanding (14, 11, 8, 5) but the sequence remains still the same , i.e., (5, 8, 11, 14) and we have to find the first term 👉 ?, 8, 11, 14 , then we gotta subtract the common difference from each term to find the first term, first term 👉 5 I mean, that's why we need to subtract So in conclusion, when u have to find the last term (sequence is in increasing order) we gotta add the common difference & when we have to find the last term (sequence goes in decreasing order), we gotta subtract the common difference from each term.
When used like it is here (as an adjective or noun adjunct), it's pronounced arithmEtic, not arIthmetic. The latter is when you're talking about the school subject -_-
Right… It’s just like Geometry. The noun form (i.e. maths subject) is of course pronounced “geOmetry”, but as an adjective in English the accent gets pushed back, e.g. a “geoMEtric” sequence. Likewise you have “aRITHmetic”, the subject or activity (a noun), versus “arithMEtic” the adjective, as in an “arithMEtic sequence”. I know this adds nothing to helping people understand things, and this chemistry tutor does a great job at that. Really, kudos to him! But it will save you from sounding silly when you go to Maths parties. Really, the best thing about Maths is the parties. 😂
![The Arithmetic Series - Part 1 - [14]](/img/n.gif)
Sequences - Free Formula Sheet: bit.ly/4eau2KQ
Sequences and Series: www.video-tutor.net/sequences.html
my math teacher did not tell us how to get the formula but instead told us to remember the formula as is. Thank you so much for the explaination
😹
Making your life easier lol😂
Our math teacher didn't even tell us the formula
Mistakes happen, but it’s good to catch them. Beautifully said
Good sir i am from somalia
i am one of your students
you are my first teacher really
long life teacher 🖐️🖐️🖐️🖐️
You have no idea how much I needed this🙏
Bruh im a new IBDP student and was so scared and confused with mai (i did not know a single thing) but now i can keep up with others so thank you deeply from my heart and wish you the best
-Arithmetic sequence is a linear function
Tn=a+(n-1)d
Tn=a+dn-d
-Sum of an arithmetic sequence is a quadratic function
C equals zero
An²+bn
na+(.5n²-.5n)d
The functions intercept at T1=S1
na+(.5n²-.5n)d
(0)a+(.5(0)²-.5(0))d=S(0)=zero
Damn bro I need to study this for my exam and videos like this make it so much easier than how my book explains it
thank you so much you are helping me so much i am physics teacher ... i was forgetting math but i have a quick reference that's you thank you again
bro i love this guy
Are u gay
Very useful. Thank you for making this video.
THANK YOU I was studying and I could not understand Why they put this worked for the life of me. They did the whole explanation of how Sn =a1 +a2 and putting it the other way around but the way the book put it was super confusing thank you so much it's like a light bulb clicked in my head.
Same! Everything was backwards and confusing in the formula book
Thanks you are first teacher really 👐👐
You are my savior 😭
DUDE I WAS JUST LEARNING THESE THANK YOUUUU !!!
Bruh same
Bruh i just wanted to revisit arithmetic
Same there
Thank you so much dear Teacher In our university level our Teacher told us to only learn this formula but not told us how to actually drive this😢😢😢😢😮 formula
just one question, what is the reason that we can add the two equations in 4:50 ?
He is adding the SAME series but in reverse order. ( see around 4.20(
This gives a new series which of course has TWICE the value of Sn ... but because one has added terms in reverse order... each term becomes a constant value - and so becomes easy to evaluate. Then to get Sn.. you divide by 2
An easy way to see this is imagine adding the simple series 1,2,3.... to say 10. ( where d =1, and n =10)
If we reverse the series and add it to each original term... we get:
10+1, 9+2, 8+3,.... 1+10.
You can easily see that this is now simply adding the constant term of 11 ten times = 110, and to get Sn we divide by 2 = 55.
Now its easy to adapt the same idea for other series with other values of difference between terms and number of terms etc as shown.
you just saved my grade bruh
I like what you are doing here!!!!
Most Needed for all... Headings
You, sir, are a LIFESAVER
I needed this in 1st semester bruh 😂 I passed with a passing grade of 85 😂
I love arithmetic progressions I already know this but I still watched it
Thank you! It's really beautiful.
Useful content 👌
My teacher didnt even teach that, its just in the exam.. and everybody knew how to do it, everyone but me. Like.. *how*
Thanks for the explanation
Thank you 😊
Hey can you do a video on combined arithmetic and geometric progression .thx
Woah it blows my mind
Thanks for this video
Thanks a lot sir
I’m trying to understand how do you know that taking the first three terms is enough to derive the formula, why not the first two? Why not just the first?
You are amazing 🤩!,,,
Thanks
As soon as you mentioned the average I was like omg...I can derive everything related to this with 2nd grade math lol
Pronounced arithMEHtic. (Different pronunciation than when you're using it as a noun.)
If I want to write a sub n in terms of a sub 1 wouldn’t that be a1 + (n-1)d? I’m just trying to understand how you changed all the other terms in terms of the first term but not a sub n
Why is no one explaining why we add them in reverse order?
شكلي العربية الوحيدة هنا😔😂
Ok I’m scared we literally just learnt about this in math methods today and now it’s on my recommendations...
Thank you very much. I understand now
Thank you soooo muchhhhh
updated 6 hours ago aaaaaa notice me please
Pls upload "how to derive formula " for all headings. *Sry bad eng
Why would you wanna complicate things and write the Sum formula from right to left
this is why the education system is wrong... and props to organic chemistry teacher for explaining why and how the formula was made that interconnects with the answers
Because we want to know where it came from not just mindlessly memorise and apply it which makes math unfun and not understandable
is it just me or the thumbnail looks like it spells the devils name?
its just you
Thanks
Hiiiii!!!!! my idol!!!!
How the f did it became s6 can somebody explain
Good
yeah, thanks
I ghat you😎
Nice
Hai
Mhm, indeed.
Why should we minus
Because we r considering the term from backwards, like
Suppose the term is
5, 8, 11, 14
So if we consider the sequence in increasing order, is that, we wanna find the *last term* , then it will go on like this 👉 5 + 3 , 8 + 3, 11 + 3 = 8, 11, 14
But if we consider the sequence from backwards , is that, we have to find the *first term* by reversing the order (for understanding) : let's say , the sequence now goes like this
👉 14, 11, 8 , 5 ; but note that the sequence still remains in it's orginal form, i.e., (5, 8, 11, 14)
as you can see, the sequence now goes like this 👉 14 - 3, 11 - 3, 8 - 3
I mean, if we reverse the order for understanding (14, 11, 8, 5)
but the sequence remains still the same , i.e., (5, 8, 11, 14) and we have to find the first term 👉 ?, 8, 11, 14 , then we gotta subtract the common difference from each term to find the first term, first term 👉 5
I mean, that's why we need to subtract
So in conclusion, when u have to find the last term (sequence is in increasing order) we gotta add the common difference & when we have to find the last term (sequence goes in decreasing order), we gotta subtract the common difference from each term.
When used like it is here (as an adjective or noun adjunct), it's pronounced arithmEtic, not arIthmetic. The latter is when you're talking about the school subject -_-
Right… It’s just like Geometry. The noun form (i.e. maths subject) is of course pronounced “geOmetry”, but as an adjective in English the accent gets pushed back, e.g. a “geoMEtric” sequence. Likewise you have “aRITHmetic”, the subject or activity (a noun), versus “arithMEtic” the adjective, as in an “arithMEtic sequence”.
I know this adds nothing to helping people understand things, and this chemistry tutor does a great job at that. Really, kudos to him! But it will save you from sounding silly when you go to Maths parties. Really, the best thing about Maths is the parties. 😂
1st
I thank you for your videos
updated 6 hours ago aaaaaa notice me please