How To Derive The Formula For The Sum of an Arithmetic Series

แชร์
ฝัง
  • เผยแพร่เมื่อ 26 ธ.ค. 2024

ความคิดเห็น • 75

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  ปีที่แล้ว +3

    Sequences - Free Formula Sheet: bit.ly/4eau2KQ
    Final Exams and Video Playlists: www.video-tutor.net/
    Arithmetic Sequences: th-cam.com/video/mxEIFO8vXKY/w-d-xo.html
    Geometric Sequences: th-cam.com/video/zJEWcysAc44/w-d-xo.html

  • @darryltang3999
    @darryltang3999 3 ปีที่แล้ว +187

    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

    • @Chipi_Chipi_Chapa_Chapa77
      @Chipi_Chipi_Chapa_Chapa77 ปีที่แล้ว

      😹

    • @1925mercy
      @1925mercy 9 หลายเดือนก่อน

      Making your life easier lol😂

    • @labridad
      @labridad 3 หลายเดือนก่อน +1

      Our math teacher didn't even tell us the formula

  • @johnboyle4161
    @johnboyle4161 2 ปีที่แล้ว +60

    Mistakes happen, but it’s good to catch them. Beautifully said

  • @Ismailbulle88
    @Ismailbulle88 3 ปีที่แล้ว +19

    Good sir i am from somalia
    i am one of your students
    you are my first teacher really
    long life teacher 🖐️🖐️🖐️🖐️

  • @unknown.exe666
    @unknown.exe666 3 ปีที่แล้ว +15

    You have no idea how much I needed this🙏

  • @HaydenJory
    @HaydenJory 2 หลายเดือนก่อน +1

    -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

  • @1inspector
    @1inspector 2 ปีที่แล้ว +3

    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

  • @Doku_Kurookami
    @Doku_Kurookami 2 ปีที่แล้ว +15

    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

  • @DanielChen-ie5mu
    @DanielChen-ie5mu ปีที่แล้ว +1

    bro i love this guy

    • @Carrymejane
      @Carrymejane 10 หลายเดือนก่อน

      Are u gay

  • @kemertube8826
    @kemertube8826 2 ปีที่แล้ว +5

    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

  • @lona3763
    @lona3763 3 ปีที่แล้ว +7

    DUDE I WAS JUST LEARNING THESE THANK YOUUUU !!!

    • @Ivanho
      @Ivanho 3 ปีที่แล้ว +2

      Bruh same

    • @akirakenchieedquiban531
      @akirakenchieedquiban531 3 ปีที่แล้ว

      Bruh i just wanted to revisit arithmetic

    • @Gbsanni
      @Gbsanni 3 ปีที่แล้ว

      Same there

  • @arjangap2551
    @arjangap2551 2 ปีที่แล้ว +5

    Very useful. Thank you for making this video.

  • @DammeeBaqqalaBadhaadhaa
    @DammeeBaqqalaBadhaadhaa 9 หลายเดือนก่อน

    Thanks you are first teacher really 👐👐

  • @stephanzoes8010
    @stephanzoes8010 2 ปีที่แล้ว +2

    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.

    • @kendalljana3275
      @kendalljana3275 2 ปีที่แล้ว

      Same! Everything was backwards and confusing in the formula book

  • @sidpenalver7602
    @sidpenalver7602 3 ปีที่แล้ว +2

    you just saved my grade bruh

  • @NazrawiSerawit
    @NazrawiSerawit 8 หลายเดือนก่อน

    Thank you! It's really beautiful.

  • @reenaznawar7004
    @reenaznawar7004 3 ปีที่แล้ว +1

    You, sir, are a LIFESAVER

  • @hirendraavenkatachalpathy8528
    @hirendraavenkatachalpathy8528 3 ปีที่แล้ว

    Most Needed for all... Headings

  • @tactical_asterisk
    @tactical_asterisk 3 หลายเดือนก่อน

    just one question, what is the reason that we can add the two equations in 4:50 ?

    • @eric4709
      @eric4709 หลายเดือนก่อน

      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.

  • @sohumsharma2892
    @sohumsharma2892 3 ปีที่แล้ว +5

    I love arithmetic progressions I already know this but I still watched it

  • @sophiedavidson1579
    @sophiedavidson1579 3 ปีที่แล้ว

    You are my savior 😭

  • @harmlesspikachu9038
    @harmlesspikachu9038 3 ปีที่แล้ว

    I like what you are doing here!!!!

  • @AmirNawaz-i1u
    @AmirNawaz-i1u หลายเดือนก่อน

    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

  • @tr4976
    @tr4976 3 ปีที่แล้ว +3

    My teacher didnt even teach that, its just in the exam.. and everybody knew how to do it, everyone but me. Like.. *how*

  • @atharvchaudhary1625
    @atharvchaudhary1625 2 ปีที่แล้ว

    Useful content 👌

  • @akirakenchieedquiban531
    @akirakenchieedquiban531 3 ปีที่แล้ว +10

    I needed this in 1st semester bruh 😂 I passed with a passing grade of 85 😂

  • @varun3282
    @varun3282 2 ปีที่แล้ว

    Thanks for the explanation

  • @mumbitsuma452
    @mumbitsuma452 2 ปีที่แล้ว +1

    Hey can you do a video on combined arithmetic and geometric progression .thx

  • @geniciaross3791
    @geniciaross3791 3 ปีที่แล้ว +1

    Thank you 😊

  • @kacy6014
    @kacy6014 2 ปีที่แล้ว

    As soon as you mentioned the average I was like omg...I can derive everything related to this with 2nd grade math lol

  • @SuongThol
    @SuongThol 3 ปีที่แล้ว

    Thanks for this video

  • @coopertownsend1371
    @coopertownsend1371 3 ปีที่แล้ว

    Ok I’m scared we literally just learnt about this in math methods today and now it’s on my recommendations...

  • @satk4211
    @satk4211 2 ปีที่แล้ว

    You are amazing 🤩!,,,

  • @zahraa.qasim5
    @zahraa.qasim5 3 ปีที่แล้ว +2

    شكلي العربية الوحيدة هنا😔😂

  • @darienwillis7652
    @darienwillis7652 ปีที่แล้ว

    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

  • @纃
    @纃 3 ปีที่แล้ว +1

    Thank you very much. I understand now

  • @reganpiano8833
    @reganpiano8833 ปีที่แล้ว

    Pronounced arithMEHtic. (Different pronunciation than when you're using it as a noun.)

  • @c.m.p2943
    @c.m.p2943 ปีที่แล้ว

    Thanks a lot sir

  • @Carrymejane
    @Carrymejane 10 หลายเดือนก่อน

    Woah it blows my mind

  • @destroyriri
    @destroyriri 3 ปีที่แล้ว

    updated 6 hours ago aaaaaa notice me please

  • @Omar-Farhat
    @Omar-Farhat 9 หลายเดือนก่อน

    Thanks

  • @hirendraavenkatachalpathy8528
    @hirendraavenkatachalpathy8528 3 ปีที่แล้ว

    Pls upload "how to derive formula " for all headings. *Sry bad eng

  • @j3v350
    @j3v350 3 ปีที่แล้ว +2

    is it just me or the thumbnail looks like it spells the devils name?

  • @lachristechnologies7639
    @lachristechnologies7639 ปีที่แล้ว

    Why is no one explaining why we add them in reverse order?

  • @filoilfigo
    @filoilfigo 3 ปีที่แล้ว

    Why would you wanna complicate things and write the Sum formula from right to left

    • @agustine1239
      @agustine1239 3 ปีที่แล้ว +2

      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

    • @mohamedtrfnx6632
      @mohamedtrfnx6632 2 ปีที่แล้ว

      Because we want to know where it came from not just mindlessly memorise and apply it which makes math unfun and not understandable

  • @leenaahmadzai6446
    @leenaahmadzai6446 3 ปีที่แล้ว

    Thank you soooo muchhhhh

  • @Creativelyrics769
    @Creativelyrics769 3 ปีที่แล้ว

    Thanks

  • @0deszuh111
    @0deszuh111 3 ปีที่แล้ว

    How the f did it became s6 can somebody explain

  • @Gbsanni
    @Gbsanni 3 ปีที่แล้ว

    Good

  • @destroyriri
    @destroyriri 3 ปีที่แล้ว

    Hiiiii!!!!! my idol!!!!

  • @bobbyb5710
    @bobbyb5710 2 ปีที่แล้ว

    yeah, thanks

  • @KundanSingh-ym4pw
    @KundanSingh-ym4pw ปีที่แล้ว

    Hai

  • @lilswiff470
    @lilswiff470 3 ปีที่แล้ว

    Nice

  • @kafulakaunda2896
    @kafulakaunda2896 ปีที่แล้ว +1

    I ghat you😎

  • @shadowf30
    @shadowf30 3 ปีที่แล้ว

    Mhm, indeed.

  • @telecommunity2181
    @telecommunity2181 2 ปีที่แล้ว +2

    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 -_-

    • @richdawes66
      @richdawes66 ปีที่แล้ว +1

      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. 😂

  • @aashsyed1277
    @aashsyed1277 3 ปีที่แล้ว

    1st

  • @nthatisimodingoane1042
    @nthatisimodingoane1042 2 ปีที่แล้ว

    Why should we minus

    • @strpa.mp4
      @strpa.mp4 ปีที่แล้ว +2

      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.

  • @magnacrushersart572
    @magnacrushersart572 ปีที่แล้ว

    I thank you for your videos

  • @destroyriri
    @destroyriri 3 ปีที่แล้ว

    updated 6 hours ago aaaaaa notice me please