Given two terms find the nth term of a geometric sequence

👉 Learn how to find the nth term of a geometric sequence. 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. A geometric sequence is a sequence in which each term of the sequence is obtained by multiplying/dividing by a common value, called the common ratio, to the preceding term.
The formula for the nth term of a geometric sequence is given by An = ar^(n - 1), where a is the first term, n is the term number and r is the common ratio. We can obtain the common ratio by dividing a term by the preceding term or if the known terms are not consecutive, we can obtain the common ratio by taking the nth root of the quotient of the two terms, where the n in the nth root is the difference of their term numbers. Plugging the required values into the formula, we can obtain the required nth term of the geometric sequence.
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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

[@dannyabifalah2753]

bless this man and his beautiful​ 6's

[@brianmclogan]

haha never knew they were different till youtube

[@tokenking6]

Aye! I'll second that motion!

[@prab3636]

after slowing this video down, and doing the math homework given to me following your steps, I've learned more in 15 minutes of you video compared to 3 whole bells of algebra. Thanks man.

[@brianmclogan]

Prabh Dhillon you are very welcome! so happy to be able to help you out!

[@melbournemeliodas215]

Prabh Dhillon i do better if I am alone with the teacher... having others slows me down, because there are too much the teacher must observe at.

[@robbinbhullar3944]

boht vadia bira good job dhillon

[@legendarysportmastercaster4536]

@@brianmclogan bless you very much and i will pass the practice homework

[@-clipz-]

God bless!!

[@theochowdry8810]

this man is the reason i am not having an anxiety attack thinking about my algebra 2 mid term

[@mattmaclean3961]

I wish i had you as my teacher

[@brianmclogan]

thanks, just trying to help as many students as I can

[@jasmineortiz1050]

matt aint loyal to his math teacher smh

[@dogbone]

@@jasmineortiz1050 lol

[@CoulRanch]

Who else is here watching this in 2097?

[@Ray-ye8gz]

Mr Brian, You could have found a14 in another way too. Since you found r=1/2, you can use the usual formula, a14= a1* r^13 ,, to get the final answer, 1000/8192 = 0.1221

[@brianmclogan]

Perfect! thank you for adding

[@pranavi1949]

But how did you know what a1 is

[@vauntyy.]

@@pranavi1949 a1 would be the first term that isn’t the initial value of a0

[@galithomas9252]

Yes A1=1000

[@reflection9924]

what does a1* mean?

[@wido4306]

everybody gangsta until brian mclogan pull up with da crazy formula

[@-clipz-]

God bless

[@user-kr2qh6in9k]

Sir, thank you. I’ve learned more in these 9 minutes than the whole year in my math class.

[@brianmclogan]

happy to be able to help you out!

[@elsdon2427]

set the speed to 2x and you can be twice as disappointed in standard education!

[@-clipz-]

God bless!!

[@Williamjohnson-jh5dq]

This doesn’t make sense

[@andresvazquez442]

Great video! confirms what I thought about solving a geometric sequence when the first term is not given.

[@precioussiete1391]

how did you simplify 6√1 over 6√64 and then ½=r??

[@wynneloveless5607]

I've been teaching for 20+ yrs and LOVE using your videos. Even when you go too fast, we can stop the show, rewind and reuse. My Army girl is now using you to increase score to promote. THANKS!

[@ChrisS-rp7yo]

Thanks helpful a on all my tests

[@earltagapolot9559]

omg i wish i had you as my math teacher

[@theDjwan]

Wouldn't just dividing two separate formulas make more sense? It would eliminate the A1 as well.

[@saminkamal3670]

doing this is 8th grade honors algebra one. Teacher didn't explain this yet. Thanks!

[@danieldrewbustillos3380]

How do you find the 1st term sir?

[@terminatorougtifv]

Thank you. Articulate and informative.

[@jennapetruniak3224]

I keep getting 1/8 after entering it into the calculator; do not understand what I'm doing wrong to get my r factor.

[@Doolin.S]

You literally just saved my homework grade😅

[@ChrisS-rp7yo]

Thank really helpful got a on all my tests

[@gavind.7918]

This guy’s amazing, my teacher is really bad and this helped a crap ton, thanks!

[@FClapp]

Wish my math teacher was this fun to learn with. A video does better than my current maths teacher

[@mdbhuiyan3238]

Thank you so much! Doing math homework used to mean staying up all night crying and praying that I would do okay on the text, but thanks to your videos,I've gone from 60/70s to 90s in college pre-calc.

[@skylight044]

Amazing....♥️
Honestly, 5/5 stars math teacher.

[@rohmanisar7091]

Can't thank you enough! I was stuck from days on this concept and your video cleared all misconceptions. Much appreciated sir!

[@clacne2541]

Does anyone know how to do this when you're only given 2 sums of two sets of terms?
For me the question is: In geometric series, the sum of the 2nd and 4th terms is 156, and the sum of the 3rd and 5th terms is 234, find the first term and common ratio

[@erionnotstar8376]

Waw! Your videos are really helpful. Since we are having our Modules because of the Pandemic. May God bless you.

[@Rachael3000]

Taught this better than my college teacher! thanks man!

[@brianmclogan]

Rachael L : ) thanks happy to help

[@uwtz4293]

Why I’m I learning this in middle school

[@hridhay5011]

lol same I'm learning this in middle school

[@colinlspencer8389]

But what would you do if the value of the nth term was a negative number

[@DANIELDALLAS_MATHs]

Hey! No problem. You can apply arithmetic, geometric and other formulae to any type of terms even if they are complex. You may watch that : th-cam.com/video/BUsE7g-4-vU/w-d-xo.html and more about sequences and lots more

[@osamugojo7541]

Wish I had you as my professor, it'll be more easy for me to understand then

[@Daniel-nm2qb]

:O You're awesome! I have four tests coming up tomorrow, so I really need to study! This helped so much! Thanks! :D

[@ManuelDaniel-vu3fp]

I really like your video.Can you hep me solve this question: 3rd term of GP is 2 and 6th term 16. Find 8th term=

[@swaminator3617]

holy crap man, i have a test later today and was lost and you helped me so much. thanks sir!

[@thorstambaugh1520]

What if the progression is formulaic with 2 variables?

[@Lennylenalenita]

6:23 fuck me that’s where I’m stuck. You can’t be stuck EDIT: Thank you, this saved my ass! Will be sharing w the rest of my group 🎉💃🏻

[@chescaparas4448]

Is he still replying? If yes. My teacher gave us the given n= 56, 4th term= 100 and 90th term = -1. We need to find for the sum of the arithmetic sequence of this☹️

[@steph_lopez]

But what its you have the first term and the 7th term and you are trying to fing the common ratio.

[@brianmclogan]

I have more videos in a playlist at the end of the video

[@maccleary9576]

God bless you and God bless the United States of America. You should run for President. Thanks for the maths assist.

[@jolinadacles8474]

what is the 2nd term of geometric sequence when the 4th term is 125 & the 5th term is 625,? Can you answer my question mr brainy?

[@johnysue3022]

Idk if you ever gonna see this but genuinely you have helped me sm through this math year you’re the best keep it up dude thanks🙏

[@dannyngcobo1837]

i liked the video but i dont understand why you must use the 10th term to find the final answer why not use the 4th term.but it all goo u still better than my teacher here in Africa.Thank You

[@zhnkbr]

is there a reason for not using simultaneous equations ?

[@manjotsihra8645]

I found it easier to just find the 1st term by dividing the 4th term by 1/2, then taking that number and dividing it by 1/2, and doing this until I reach the first term. It didn't take that long to do either, because of its simple division. I then used the 1st term in the formula and it got me to the same answer.

[@brianmclogan]

thanks for sharing Manjot!

[@Hapi_smiley]

dude this guy is the goat i have a math exam tomorrow and i didn't get the lesson in 4 hrs of math class, and this guy managed to teach me in 9 mins

[@Aretim5882]

Wow Logan I like that way. That I want to use a calculator on my phone for this. Well I think thank you

[@kcmouli8766]

U are very active sir

[@AlexMalex533]

anybody else just doing math at 2 am cuz ur procrastinating an ur about to fall asleep

[@adgf1x]

r^6=1/64=(1/2)^6=>r=1/2,=>14th term=10th*r^4==125/64.8=125/512ans

[@angel1202003]

the ratio of the third and first term does not give you the answer of what the second term would be. he lied

[@landonschannel6769]

I have a question like this in my text book but it's asking me to solve for the first term. How would I do this?

[@brianmclogan]

instead of plugging in 14 you would plug in 1

[@anglerfiishy470]

my head actually aches after learning this but TYSM

[@rainnier7514]

After 3:11 I can't understand what did he do. Can someone explain to me?

[@mannatbaveja5989]

Can you do a problem where you are given for example, the first and the sixth term of a geometric sequence and you need to find the tenth term? And this video really helped me understand a lot of geometric sequences!

[@jtigers5123]

Thank you for providing your teachings.

[@paelchoy8780]

Just like what he did to find A14, we can also find A1. which is 1000

[@kendrickdo7943]

why the ffffff- bruh I learn more here then my whole one class of Algebra 2 lmao

[@ryahbaroudi6351]

I'm getting ready for an exam for my precalc class that I haven't been able to attend for 3 weeks, so these videos are saving me. Thank you.

[@brianmclogan]

awesome! happy to help, good luck on your exam

[@MrCarterVince]

if the 5th term is 3 and the 14th term is 1536, how can i find out the value of the 9th term?

[@brianmclogan]

kevin mao need to determine the explicit formula also determine if it is geometric or arithmitic

[@MrCarterVince]

Mr. McLogan's Math Channel thanks, i will take a look at the question

[@siddhantkurian4987]

Ceo of helping my dumbass understand math

[@raphaelencila3564]

Sino andito dahil sa modules?

[@wesleywride1837]

Thank you so much. I have to finish a math class before I can go out on a date with a girl. And my parent's would've made me cancel if I didn't finish. I couldn't have finished without this video. Thank you. So Forking Much

[@brianmclogan]

You're so welcome happy to help you date haha!

[@heradelossantos5092]

I'm so dumb jejje so why is r 1/2 and not 1/8

[@Evemiela]

how would you find the 1st term?

[@brianmclogan]

just find the formula then you can find any term

[@tokenking6]

Thanks for all the great info!

[@leclerc_1652]

Life saver!, this technique wasn't even given in my textbook. Thank you so much!!!

[@detectivex9210]

I'm grade 10 now and I found out what the a sub 1 is. I don't know if it is correct but my answer is 1000. I divided enumeration to denominator (125/64) resulting 1.95. And from the 4th term I tried to divide it by 2 as well and I made it through 1.95 so if the 4th term is the half of its past term maybe I could add 4th term itself and made it to 1st term.

[@princessjessebelclaritoabm9293]

I HAVE NEVER BEEN SO HAPPY AND SO GRATEFUL THAT SUCH A WONDERFUL HUMAN BEING SUCH AS YOU, SIR/PROFESSOR MCLOGAN EXISTS IN THIS WORLD FULL OF UGLY THINGS. THANK YOU SO MUCH FOR SAVING ME AND ALL THE OTHER STUDENTS FROM FAILING. THE WAY YOU TEACH IS JUST SO GENIUS THAT EVEN AN IDIOT LIKE ME CAN UNDERSTAND. THANK YOU SIR! YOU ARE VERY MUCH APPRECIATED BY YOUR VIRTUAL STUDENTS/US. MAY YOU HAVE ALL THE LOVE, HAPPINESS, AND KINDNESS THAT YOU DESERVE. THANK YOU!

[@sherylsibay6919]

So im watching this because of module

[@arnaufernandez8572]

dude u saved my life man i have exam tmwr and didnt understant anything after 3 weeks of class, and u manage to teach me in 9min
THANK YOU

[@7wolfgaming710]

great video explains a point clearly

[@yxngboidee2145]

Mr Goetzinger, aint dat u?

[@guinereyes2463]

Omygosh I'm so happy, finally I found the most understandable video. THANK YOU SO MUCH 🥰

[@BadassMotherFucker]

Thank you so, so very much for opening my mind up to the 6th factor.!! Is there any way to just jump from the 6th straight to the 14th?!? J/K, I know that’s not possible but it would be fun to think so, lol!! Thanks again Aaron Jesse💯

[@VLT.]

Who here has a math final…?😃

[@zul2788]

So to find a1, all I had to do is plug in all found variables and solve it normally right? Only reason you chose to go for a14 = a10(r)4 is because its quicker and less time consuming?

[@alemmypadua1229]

Thanks I learned something and it is easy to learn.Love it cause you know I am bored with other tutor..I can't understand what they are saying....

[@manuelenriquez9589]

this is a life saver 1 day before your test 😂

[@lovelynjoygatila1029]

What if the Given is A sub3= 4/5 and A sub9=1/80 find the common ratio and A sub 1

[@ayaanmumtaz2007]

Thank you sir , it helped me a lot

[@roxarianoroxas7212]

heaven sent!!! quarantine got me blended learning im on philippines and here tis vid helped so much bcuz my teacher has no net all the time and were forced to learn ourselves...

[@elijahsalinas1039]

who else gets the ThatTutorGuy.com ads with Brian

[@ziwasafira418]

M writing my engineering mathematics tomorrow and this has really helped alot 🙏🙏🙏 thank you

[@jasonnwaobi430]

Bless this teacher fr, but respectfully that girl needed to shut up.

[@brianmclogan]

🫢🫢🫢

[@jasminelie1600]

Huhu...Finally, I answered my assignment .... Thank you very muchhh

[@yanxiaw2931]

Hii need help here
Q : the first term of the geometric progression is a and the sum of the second and third term is 6a/25
How do I find the common ratio?

[@NioFiota]

i hope you know your videos are still helping kids all these years later, good job

[@SaadTheGlad]

Who is he talking to?

[@alftupper9359]

I'm sure if you were to speak a little slower, you would get more hits/likes.

[@brianmclogan]

Probably, I know I need to slow down at times, appreciate the feedback, FYI you can slow down the video on TH-cam if that helps at all

[@jydeosaure6564]

what if they're both fractions

[@emilialuoma3398]

Thanks, you just saved me from my mental breakdown

[@brianmclogan]

Boom!

[@ChickenAlliance]

2:12 blew my mind

[@brianmclogan]

😀

[@sergionieto9170]

Had to come to your great videos to teach me this in 5 minutes while my professor gives me homework with stuff she has never taught me before

[@sarahhill7140]

Thank you so much!!! I literally knew how to do all my problems after this. Amazing!!!

[@iviwemndi176]

This is very helpful and thank you... but can you make a video about finding the general sequence and not a specific term

[@spartanrabbit]

dude you are awesome!! really! :)

[@brianmclogan]

happy to help

[@koseakalema2290]

Thanks a lot my best teacher I had failed but indeed your best to me

[@michaelangelotorrevillas4951]

mr brian you couldve used the 4th term to solve the a1 and not complicate the solution a1 is 1000

[@brianmclogan]

true

[@theellaphant.]

tysm

[@stvndnh1071]

why do you teach better than my pre-cal teacher... she has a masters in engineering.