Finding the formula for a sequence of terms

👉 Learn how to write the rule of a sequence given a sequence of numbers. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence.
To write the explicit formula of a sequence of numbers, we first determine whether each term of the sequence is obtained by adding/subtracting a common value to the preceding term or whether each term of the sequence is obtained by multiplying a pre-determined value, called the common ratio, to the preceding term or neither.
For the first case, the sequence is an arithmetic sequence and we can write the explicit formula by plugging the common difference into the arithmetic sequence explicit formula. For the second case, the sequence is a geometric sequence and we can write the explicit formula by plugging the common ratio into the geometric sequence explicit formula. For the third case, we can examine the pattern and by some kind of trial and error, we can be able to write the explicit formula.
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Organized Videos:
✅ Sequences
• Sequences
✅Sequences | Learn About
• Sequences | Learn About
✅Determine The First Five Terms of The Arithmetic Sequence
• Determine The First Fi...
✅How to Write The Formula for a Arithmetic Sequence
• How to Write The Formu...
✅Find the nth Term of an Arithmetic Sequence
• Find the nth Term of a...
✅Find the First Five Terms of a Geometric Sequence
• Find the First Five Te...
✅How to Write The Formula for a Geometric Sequence
• How to Write The Formu...
✅Find the nth Term of a Geometric Sequence
• Find the nth Term of a...
✅How to Determine Arithmetic or Geometric Sequence
• How to Determine Arith...
✅Find the First Five Terms of a Sequence
• Find the First Five Te...
✅How to Write The Formula for a Sequence
• How to Write The Formu...
✅Find the nth Term of a Sequence
• Find the nth Term of a...
✅How to Simplify Factorials
• How to Simplify Factor...
✅Recursive Sequences
• Recursive Sequences
✅Prove the Sum by Induction
• Prove the Sum by Induc...
✅Find the Given Term of Binomial Expansion
• Find the Given Term of...
✅Binomial Expansion | Learn About
• Binomial Expansion | L...
✅How to Expand a Binomial
• How to Expand a Binomial
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👨‍👩‍👧‍👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: www.freemathvi...
#sequences #brianmclogan

[@Shiftheads1]

He is the Jonny Sins of calculous

[@DiptayanBanerjee]

C'mon!

[@Shiftheads1]

@Leland Hugh I care

[@yondio968]

Jonny sines

[@danilomoviescenter5787]

I like the way you explain him....

[@adoni-tr3pq]

Dont waste ur time on that shit Study for ur betterment

[@jiis4kookonly811]

If we only have a teacher like that in which we can ask freely if we have question😢

[@mohamadelharakeh6441]

this will be my last video of this semester . thank you so much for all the work you put in your videos .. you were more helpful than the teacher i paid to be .. again thanks so much for every video you did.

[@qalba3016]

No no no this is very wrong -1(1)*2+(-2)= 0 regardless of these theories it’s an accident because if you only change 1 number or add to one of them it’s NOT going to add up as explained

[@adityamodi7995]

@@qalba3016 try again and see dumb**. what he taught is accurate.

[@charisegumapac3609]

I really love your videos. All the lessons that I can't understand makes sense now after watvhing yours. Thank God I have someone to learn more from!Thanks Brian💗 -from Philippines

[@spooksmeister309]

Thank you Mr. Logan! I have always looked to you for help since 2 years!

[@brianmclogan]

well really appreciate your loyalty and the fact I have been able to help for so long

[@alnajoyligsanan1581]

Thank you 😌😍💞❤️💗 and good bless

[@lolliz100]

That last question that student asked at the end was my concern as well.... Which is: Is there another way of figuring out the Formula other than trying arbitrary methods until it works. Lol. I was hoping that the general format of Arithmetic Progression or Geometric Progression would always easily manifest the formula, but after watching many videos, I've seen that what you all have in common is just trying different operations and mix of operations until it gives rise to the progressing terms. So I guess I can conclude that's the nature and approach of the topic Sequences & Series. But this was nicely reasoned out though, Thankyou.

[@raghadkhaled6890]

Thanks

[@yourfavlightskin2903]

The love i have for this teacher I hope he is my algebra 2 teacher I bet he would be the smartest teacher in our school 😂

[@YimengandCharles]

wow the patience you have with those questions I would lose it

[@average_is-2749]

This man is a god

[@javeedmuhammad4233]

The fuck?

[@wachowski9525]

@@javeedmuhammad4233 Whenever someone says something so drastic it's almost scary lol, what's going on in that head y'know

[@ankitbhandari4130]

Thank you for yrs valuable information sir .keep it up.

[@thisrandomdude_]

Woah. Mind blown. This was so interesting to learn! I'm sure it'll come in handy next year, when we deelve deeper into arithmetic series.

[@megsalex4017]

What about this problem... Gregor has decided to create a new sequence that starts with the numbers 4,1,5,6,11,... where each term after the first two terms is found by adding the two previous terms. On the 25th term, his addition was off by . That is, the sum was 1 greater than the correct one. If he made no other mistakes, how far off was the 35th term? Term 1 = 4Term 2 = 1Term 3 = Term 1 + Term 2 = 4 + 1 = 5Term 4 = Term 2 + Term 3 = 1 + 5 = 6Term 5 = Term 3 + Term 4 = 5 + 6 = 11 Thank you so much if u can help I’m just so confused I don’t know at all what to do

[@brianmclogan]

sorry just have time to focus on what I am currently teaching

[@dinkmalone9065]

what are you currently teaching

[@carlik3974]

How do I find an when the sequence is increasing by a power? 18,20,24,32,48

[@dronecinematic7262]

carli K 2^n+16

[@simplydannie]

@wow turtle rabbit kim huh?-

[@renan6827]

Learning it right now. Thank you

[@sarahmohammed5185]

He's a master

[@conordonovan1373]

This dude is awesome, serious math teacher vibes too haha

[@iyajaydeduenas8608]

Thanks you save my grades 😊

[@axldrewvarca5047]

Thank you 💕 for learning

[@jeanroseromo4422]

What if sir Everything is positive but the same term that u give?

[@mehdihouasse4951]

ROSE JEAN , you don’t multiply by (-1)^n

[@notsurewhattoputhereyet7052]

whoever kept interrupting him was really annoying.

[@sarahmohammed5185]

I know right

[@xLeroi]

Don't worry I stabbed her

[@lollol-rn9kp]

@@xLeroi thank you for doing gods work 🥰

[@ed6393]

Really good inductive approach. Thank you for uploading

[@shaneglass3576]

Your students are mind-numbing

[@jianez7141]

todos latam se lo agradece señor

[@Dr.PayalHiranwar]

I like your way of teaching. Mine is also the same. I like students asking me doubts in the class. It's only then that their concepts get cleared. I am from India 🇮🇳. You are doing great Job👌

[@alrayhankamal7187]

Can someone tell me the meaning of the (-1)^n? Pls?

[@ksitings763]

So basically if u do -1 to the power of any odd number, u will get -1. If u do it to the power of any even number, u will get 1. (-1)^n is only used for sequences that have both positive and negative numbers

[@princessmaybriz1367]

you helped me a lot, thanks!

[@subhojithalder2814]

Can it be (-1) ∆(n-1) (n∆2+1) Jst asking that (n+1) can be (n-1)?

[@professorthanos1138]

How can I find the answer to 1, -4, 9, -16, 25? I kinda understand the video but how can i find the explicit formula to the question above?

[@brianmclogan]

looks like you are dealing with square numbers n^2 and alternating signs (-10)^n

[@professorthanos1138]

Brian McLogan i have a math homework and the question is find a sub 8 in each of the following sequences and im really confused on how to find the answer

[@brianmclogan]

not sure what sub 8 means

[@remupantoja9302]

maybe plug in 8 to it

[@giselindeanguwo6283]

Good teacher

[@VijaySingh-bh8go]

How do you find the quadratic sequence with only the 2nd term and 4th term to

[@brianmclogan]

I believe I have a couple of videos on geometric sequences that will help just search my channel "geometric sequences"

[@xyfinedaydreamer3130]

You enlightened my mind thank you much😊👍

[@brianmclogan]

you are very welcome!

[@konnos06]

Is there another way of representing instead of (-1) to the power of?

[@brianmclogan]

It must me negative for the alternating signes

[@shenshen1161]

what is its common difference?

[@khriss7790]

D

[@fufu3768]

Hi, quick question. Where did the "2+1" on the second term went?

[@Dr.PayalHiranwar]

2+1 =3 and (-1) to the power 3 will give "negative 1". Odd powers of (-1) will always give ( -1). And Even powers of (-1) will give value 1

[@izzahzamri2267]

FINALLY!!!!!NTHANKS A LOT SIR!!!!!

[@ahmux4506]

Thank you

[@ashanticarter8537]

How do you do it by finding the 52nd term satrting with 4

[@brianmclogan]

Depends on the type of sequence, here is my playlist for arithmetic and geometric kzbin.info/aero/PL0G-Nd0V5ZMpQxNU0stxlxgHLxYY-Rq1b kzbin.info/aero/PL0G-Nd0V5ZMpZTW9A9qe6JnfyyTwXOaY0

[@Amer54405]

You have a mistake in the bigining you should multiply by (-1)^(n+1)

[@relentlessalwin8850]

thankfull

[@yachoooo1748]

I lovvvvveee you you just save my day

[@firozahmad6181]

Thank you!!

[@rayhanrani3857]

bro this class

[@lucirius1773]

Thank youuuuu you help alot..

[@jonreyobus8608]

Thanks po

[@davidhashemiannik678]

Thank You, helped me so much.

[@brianmclogan]

you are very welcome!

[@atizadoeric8213]

Its really help

[@programmer9310]

Please I need explain how to solve the sequance : O, t, t, f, f, s, s 😢

[@sartorio9129]

thank sir Johnny Sin

[@patrickmayer9218]

Calc 2 goes brrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr!

[@justblue9379]

How did u find your n's though?

[@TheQuancy]

Generally we always start with n=1 so, n is usually 1,2,3,4,5,6.... etc n doesnt matter because whatever number u plug in, should result in the same pattern

[@keithannsosa6130]

thankyouuu so muchhh

[@RandomTot]

Omg thank you

[@amac2813]

I have a CFP and this is complicated

[@1XXAylinXX]

purrrr my college professor could never and chatgpt gets those random errors ugh

[@divergentmaths]

2 - 5 + 10 - 17 + 26 - 37 ± … = 1/2

[@sensui4466]

(n-1) - n(n+1) is another formula for this sequence

[@arulgk9673]

rheaa Yeah that works too

[@barrydavis331]

No, it does not work. Input 1 gets output -2 (wrong) (1-1) -1(1+1) = 0 -1(2) = 0 - 2 = -2 Input 2 gets output -5 Input 3 gets output -10 (wrong)

[@losanentombimaleka9787]

Im struggling with -6;...; 3 ;...; 15

[@drewelliott3132]

there's always that one person in class that won't stfu lol

[@user-bg4ig8ct5x]

He looks like Randy Orton

[@sultown4343]

Student who kept raising ideas would understand if she just listened for 2 minutes 💀

[@6c15adamsconradwilliam3]

4:00 “-1 squared is? ... -1”

[@Chama0398]

Answer Is +26

[@francisrafaelpuertas7145]

There's magic

[@iiiimaaaan]

2, -5, 10, -17..... Is -20

[@adgf1x]

Formula=2+(n-1)*-7=9-7n

[@ghostfrom1950]

So you're saying this is a bunch of trial and error? GREAT

[@meowzxfjxf5412]

Yasssss

[@melancholiac]

Personally, I think his explaining is crap. Kept losing me.

[@brianmclogan]

Happens, sorry about that, I have a lot of videos some good, and as you noted, some not so much

[@melancholiac]

Mate, you win some, you lose some. Plenty of people enjoyed your lecture, I just didn't. Horses for courses.

[@PSALMS413]

i for sure have a learning disability

[@brianmclogan]

Keep walking you got this

[@edmariotorio8271]

Its wrong -1square is still -1

[@sparguspargu7014]

Negatives with exponents that are even numbers give you a positive. So -1^2 = 1

[@adrianrainierfabian1852]

-1 x -1 =1

[@simplydannie]

Edmario.. A if you mutliply a negative with another negative, it will be a positive.

[@boccaluppo930]

This professor s attitude is condescending. ugh