Sum of an Arithmetic Series Formula

Learn how to find the sum of an Arithmetic Series in this free math video tutorial by Mario's Math Tutoring. We discuss use of the sum formula and go through some example problems.
0:17 Difference Between a Sequence and a Series
0:28 Formula for Sum of an Arithmetic Series
0:40 Example of Why and How the Formula Works
2:25 Example 1 Finding the Sum of an Arithmetic Series in Summation (Sigma) Notation
3:49 Trick for Finding the Number of Terms in a Summation
4:57 Example 2 More Challenging Example
5:40 Using the Explicit Formula for an Arithmetic Sequence
Related Videos:
Arithmetic Sequence Explicit Formula
• Arithmetic Sequence - ...
Playlist for Sequences and Series
• Sequences & Series
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[@SUPERSAVERHEROgamer]

This was actually so beautiful, the way you explained how the formula works and why it works.

[@bleepbloop2242]

thank you for explaining why the formula is the way it is, it always helps me as it suits my way of thinking

[@d.rabbitwhite]

Exactly. Otherwise, just memorizing formulas, I get caught up trying to figure out the whys , and go down a rabbit's hole of frustration.

[@gabombisabajombi7371]

Thank you so much, after watching this I just finished my assignment easily! I learned a lot from this 6 minutes than I had for 30 minutes in school.

[@jarridkamphenkel2117]

Best video on the topic! thank you for using an uneven number example and showing how the numbers actually work!

[@jenajilbadiong6690]

thanks for the formulas, i don't even understand my modules ajskshs

[@aphroditeg-10amarilloartvi6]

Mare tulong char

[@tolentinotabanao9651]

Adding sum a/n

[@jewelmonsta1342]

Such a brilliant video, best explanation ever. Thank you!!

[@MariosMathTutoring]

+Jewel Monsta your welcome! Glad the video helped you.

[@jacobgriner9569]

love your videos man. hope you get more publicity with the amount of great material you post.

[@MariosMathTutoring]

Thanks a lot! I appreciate that! Glad my channel is helping you with your math!

[@sydniesy7922]

For me, I won't divide 17 yet, I will get the answer first in the a sub 1 and last term, then I'll multiply that answer to 17 then divide it to 2 so it's like s17= 17/2 (14+62) = 17/2 (76) = 1292/2 so 1292÷2 is 646 so the answer is 646

[@sydniesy7922]

I mean this is a long method for me since my adviser said if you got an answer with a .5 or something you shouldn't continue it and let it stay the way it is then just prioritize the a sub 1 and last term then do the division after that, we don't use calculators so this is how you could answer it without calcu.

[@miyuki6541]

@@sydniesy7922 same answer with when i computed it the answer is 646.

[@sethcarter454]

I love your teaching skillsss

[@poyut]

thank you, so helpful. subscribed

[@christianprinceranara1017]

the best video ever, easy to understand and very simple, keep it up sir. Thank you.

[@rickgrimes2079]

I have 2 say ur helping me more than my teacher please keep doing this tnx

[@nio.ngaming9775]

THIS WAS HELPFULL

[@josephkasai9794]

Best explanation ever any reference book please

[@farheennza]

thank now i understand formula

[@michaelli4331]

U are brilliant!

[@user-rz9qf7qh2d]

Thank you!!!!!!

[@aidx2942]

thanks so much

[@alperenkrst4799]

thank you so much

[@jaylu1878]

Nice video sir...thanks because it helps me to solve faster the problems at math

[@ASkruger]

Thank you, you are a legend.

[@trevorpope1913]

Excellent video, thank you

[@ankitaaarya]

Who ever thought of the first formula in that way is sooooo clever and brilliant

[@Brianna-meza]

Thanks!

[@MariosMathTutoring]

Thank you!!

[@pizzadog1847]

Thank you!

[@MariosMathTutoring]

You’re welcome Cyris!

[@Thefarnworth1]

Another great one, thank you.

[@territeresita]

Thank you! You’re awesome!!!

[@wnJhntn]

Fantastic

[@MariosMathTutoring]

Thank you so much 😀

[@janella6456]

Thank you sir. It helped me a lot. But what if the given sequence is in descending order. How would it be? Hoping you notice this comment

[@alexiagabriel1724]

Thank you for this.

[@espitachristineaudreydyana9443]

You save me huhu

[@sus6616]

absolute goat

[@xyz-vl8ri]

Thank you, sir!

[@FYLPOC]

God bless you

[@BurNJoE]

thank you sir!

[@micahraney732]

Great visual explanation of the formula! But, the answer should be 646 by my calculation.

[@nico_lodeon2032]

do you have a video about how to get the n if you already have the sum, first term and last term?

[@TheRatedRSuperstar11]

You’re way better then my math professor lmao

[@keshiaduplooy119]

You. Are. Amazing. Thank you so much for this 💕💕

[@MariosMathTutoring]

You’re welcome! Glad you liked my video!

[@nicolewu2050]

OOooooOOo I understand now

[@jeremyalbero1445]

Thanks

[@MariosMathTutoring]

You’re welcome Jeremy!

[@QuangNguyen-kb4ip]

Thank you for your explanation but it seems the problem I'm trying to solve is a bit more tricky:
The first eight terms of an arithmetic series have a sum of 148. The common difference is 3. What are the first three terms of the series?

[@ibrahimsemanu1511]

@Quang Nguyen
The first 3 terms are 8,11 and 14

[@QuangNguyen-kb4ip]

@@ibrahimsemanu1511 thank you

[@steveharvey3582]

Sir what if the given sequence is
½,-⅓,-¾,-1,-7/6
How can I find the Sn? What formula do I need to use?

[@katherinmaepapellero8419]

Where did you get that 20? In S20?

[@cm9154]

what if the last term is a negative do we subtract?

[@nobodyunknown4905]

You have a resemblance with Tom Ellis the main character in Lucifer.
Both handsome

[@nycaashleedemanarig3227]

how about sir the arithmetic series of 3 plus 5 plus 7 plus 9 plus 11.?

[@snissen3]

Does this formula work if there is an integer in the equation....Ex: Sum (n squared +2) n=1 to 6

[@MariosMathTutoring]

Stephen the formula I show in this video is just for arithmetic series...you can review sequences and series and learn about the formulas in this video I did here: Sequences and Series (Arithmetic & Geometric) Quick Review ua-cam.com/video/Tj89FA-d0f8/v-deo.html

[@asssreddy]

excuse me, what if the difference if the sequence was a negative number?

[@evangelinebacalso5227]

Hi sir, what if d and n are missing?

[@windhamza]

Had to send this to my gf
Can't believe I'm a topper and i can't teach others what I've learned xD

[@umopapisdn466]

I shit my pants

[@primeguy6547]

me to

[@oxy1097]

go /unshit to unshit your pants! you're welcome!

[@anisamohammadi4176]

Thank you very much,just your writing is very small and not clean this is make problem to understand

[@MariosMathTutoring]

Ok, thank you

[@atizadoeric8213]

What if a1=5.2,a7=16
And d=?

[@malloriereyes3046]

Why did you put the an as 100 ? Is it because it is the last number ?

[@MariosMathTutoring]

Yes Mallorie....when you use the sum formula you need the value of the first term plus the sum of the last term in the series then multiplied by the number of terms divided by 2. Hope that helps you!

[@malloriereyes3046]

@@MariosMathTutoring thank you so much that helped alot !!

[@MariosMathTutoring]

Ok great! Glad that helped!

[@jesskiller2461]

how does it equal to 57 if its 2+3 (19)

[@gorgieeebeauty7661]

Macel Lim it's 59

[@top8137]

I dont get how you are determining what n is.

[@MariosMathTutoring]

Are you referring to the first example? n represents the number of terms in the series so if the summation shows an index of 4 on the bottom and a 20 on top there are 17terms in the series. (20-4+1 since you are counting the first and the last term). Hope that helps...

[@KrishnaKrishna-ib6xu]

u fucking godd

[@wqeqwsaffdg1696]

why is there sigma in math