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

Поделиться
HTML-код
  • Опубликовано: 9 сен 2024
  • This video explains how to derive the formula that gives you the sum of an arithmetic series. This video also explains the difference between an arithmetic sequence and an arithmetic series as well as identifying the common difference between terms.
    Access Full-Length Premium Videos: / mathsciencetutor
    _______________________________________________________________________________________________
    Algebra For Beginners: • Algebra For Beginners ...
    Algebra 1 Review Study Guide: • Algebra 1 Review Study...
    Algebra Final Exam Review: • Algebra Final Exam Review
    Pre-Calculus Final Exam Review: • Precalculus Final Exam...
    ________________________________________________________________________________________________
    How To Evaluate Algebraic Expressions: • How To Evaluate Algebr...
    Fractions - Basic Introduction: • Fractions Basic Introd...
    How To Solve Linear Equations: • How To Solve Linear Eq...
    Linear Equations - Test Review: • Linear Equations - Alg...
    How To Factor Trinomials: • Factoring Trinomials T...
    Systems of Linear Equations - 2 Variables: • Solving Systems of Equ...
    Quadratic Equations - Test Review: • Quadratic Equations Mu...
    Multiplying Rational Expressions: • Multiplying Rational E...
    Graphing Rational Functions: • Graphing Rational Func...
    Radical Expressions - Test Review: • Simplifying Radical Ex...
    Logarithms Practice Problems: • Logarithms - Practice ...
    Functions and Graphs - Practice Problems: • Functions and Graphs |...
    How To Graph Equations in Algebra: • How To Graph Equations...
    Functions - Test Review: • Functions
    ________________________________________________________________________________________________
    Conic Sections - Basic Introduction: • Conic Sections - Basic...
    Finding The Radius and Center of a Circle: • How To Find The Center...
    Writing Equations and Graphing Circles: • Graphing Circles and W...
    Writing Equations of Ellipses: • Writing Equations of E...
    Circumference of an Ellipse: • Circumference of an El...
    Area of an Ellipse: • Area of an Ellipse
    Eccentricity of an Ellipse: • Eccentricity of an Ell...
    Hyperbolas - Conic Sections: • Hyperbolas - Conic Sec...
    Parabolas - Focus and Directrix: • Finding The Focus and ...
    How To Find The Vertex of a Parabola: • How To Find The Vertex...
    Conic Sections Quiz: • Conic Sections Quiz - ...
    ________________________________________________________________________________________________
    Arithmetic Sequences: • Arithmetic Sequences a...
    Geometric Sequences: • Geometric Series and G...
    The Fibonacci Sequence: • Mathematics - Fibonacc...
    Arithmetic, Geometric, & Harmonic Mean: • Arithmetic Mean, Geome...
    Probability - Basic Intro: • Introduction to Probab...
    Intro to Statistics: • Introduction to Statis...
    _______________________________________________________________________________________________
    GPA Calculator: • How To Calculate Your ...
    Student Loans: • How To Calculate Your ...
    Save Money In College: • How To Save Money and ...
    SAT Test Prep: • Evaluating Functions a...
    ACT Test Prep: • ACT Math Test Prep

Комментарии • 69

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  8 месяцев назад +2

    Final Exams and Video Playlists: www.video-tutor.net/
    Arithmetic Sequences: ruclips.net/video/mxEIFO8vXKY/видео.html
    Geometric Sequences: ruclips.net/video/zJEWcysAc44/видео.html

  • @darryltang3999
    @darryltang3999 2 года назад +171

    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

  • @johnboyle4161
    @johnboyle4161 2 года назад +56

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

  • @Ismailbulle88
    @Ismailbulle88 3 года назад +19

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

  • @Robo-Girl123
    @Robo-Girl123 3 года назад +14

    You have no idea how much I needed this🙏

  • @1inspector
    @1inspector Год назад +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 года назад +14

    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

  • @kemertube8826
    @kemertube8826 2 года назад +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

  • @arjangap2551
    @arjangap2551 2 года назад +5

    Very useful. Thank you for making this video.

  • @stephanzoes8010
    @stephanzoes8010 2 года назад +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 года назад

      Same! Everything was backwards and confusing in the formula book

  • @DanielChen-ie5mu
    @DanielChen-ie5mu 9 месяцев назад +1

    bro i love this guy

  • @sohumsharma2892
    @sohumsharma2892 3 года назад +5

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

  • @user-mu6ts7kr2w
    @user-mu6ts7kr2w 5 месяцев назад

    Thanks you are first teacher really 👐👐

  • @lona3763
    @lona3763 3 года назад +7

    DUDE I WAS JUST LEARNING THESE THANK YOUUUU !!!

  • @NazrawiSerawit
    @NazrawiSerawit 4 месяца назад

    Thank you! It's really beautiful.

  • @reenaznawar7004
    @reenaznawar7004 2 года назад +1

    You, sir, are a LIFESAVER

  • @Carrymejane
    @Carrymejane 6 месяцев назад

    Woah it blows my mind

  • @hirendraavenkatachalpathy8528
    @hirendraavenkatachalpathy8528 3 года назад

    Most Needed for all... Headings

  • @akirakenchieedquiban531
    @akirakenchieedquiban531 3 года назад +10

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

  • @sidpenalver7602
    @sidpenalver7602 3 года назад +2

    you just saved my grade bruh

  • @tr4976
    @tr4976 2 года назад +3

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

  • @harmlesspikachu9038
    @harmlesspikachu9038 3 года назад

    I like what you are doing here!!!!

  • @sophiedavidson1579
    @sophiedavidson1579 2 года назад

    You are my savior 😭

  • @Omar-Farhat
    @Omar-Farhat 6 месяцев назад

    Thanks

  • @geniciaross3791
    @geniciaross3791 3 года назад +1

    Thank you 😊

  • @magnacrushersart572
    @magnacrushersart572 Год назад

    I thank you for your videos

  • @varun3282
    @varun3282 2 года назад

    Thanks for the explanation

  • @mumbitsuma452
    @mumbitsuma452 2 года назад +1

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

  • @c.m.p2943
    @c.m.p2943 Год назад

    Thanks a lot sir

  • @SuongThol
    @SuongThol 3 года назад

    Thanks for this video

  • @reganpiano8833
    @reganpiano8833 9 месяцев назад

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

  • @user-qw4vg9lf5v
    @user-qw4vg9lf5v 3 года назад +1

    Thank you very much. I understand now

  • @atharvchaudhary1625
    @atharvchaudhary1625 2 года назад

    Useful content 👌

  • @satk4211
    @satk4211 2 года назад

    You are amazing 🤩!,,,

  • @leenaahmadzai6446
    @leenaahmadzai6446 2 года назад

    Thank you soooo muchhhhh

  • @Creativelyrics769
    @Creativelyrics769 3 года назад

    Thanks

  • @darienwillis7652
    @darienwillis7652 Год назад

    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

  • @kacy6014
    @kacy6014 2 года назад

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

  • @coopertownsend1371
    @coopertownsend1371 3 года назад

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

  • @bobbyb5710
    @bobbyb5710 2 года назад

    yeah, thanks

  • @Gbsanni
    @Gbsanni 3 года назад

    Good

  • @riannegliocam7713
    @riannegliocam7713 3 года назад

    updated 6 hours ago aaaaaa notice me please

  • @hirendraavenkatachalpathy8528
    @hirendraavenkatachalpathy8528 3 года назад

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

  • @lilswiff470
    @lilswiff470 3 года назад

    Nice

  • @kafulakaunda2896
    @kafulakaunda2896 Год назад +1

    I ghat you😎

  • @lachristechnologies7639
    @lachristechnologies7639 Год назад

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

  • @zahraa.qasim5
    @zahraa.qasim5 2 года назад +2

    شكلي العربية الوحيدة هنا😔😂

  • @riannegliocam7713
    @riannegliocam7713 3 года назад

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

  • @j3v350
    @j3v350 3 года назад +2

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

  • @0deszuh111
    @0deszuh111 2 года назад

    How the f did it became s6 can somebody explain

  • @KundanSingh-ym4pw
    @KundanSingh-ym4pw Год назад

    Hai

  • @filoilfigo
    @filoilfigo 3 года назад

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

    • @agustine1239
      @agustine1239 2 года назад +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 года назад

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

  • @shadowf30
    @shadowf30 3 года назад

    Mhm, indeed.

  • @telecommunity2181
    @telecommunity2181 2 года назад +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 Год назад +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 года назад

    1st

  • @nthatisimodingoane1042
    @nthatisimodingoane1042 Год назад

    Why should we minus

    • @strpa.mp4
      @strpa.mp4 Год назад +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.

  • @babarazamsucks
    @babarazamsucks 3 года назад

    First

  • @riannegliocam7713
    @riannegliocam7713 3 года назад

    updated 6 hours ago aaaaaa notice me please