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

[@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]

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[@-clipz-]

God bless!!

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bless this man and his beautiful​ 6's

[@brianmclogan]

haha never knew they were different till youtube

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Aye! I'll second that motion!

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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

[@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?

[@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!!

[@FClapp]

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

[@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

[@NioFiota]

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

[@andresvazquez442]

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

[@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!

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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

[@rohmanisar7091]

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

[@jtigers5123]

Thank you for providing your teachings.

[@leclerc_1652]

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

[@watamelon9622]

This man's explanation is very understandable.

[@brianmclogan]

Happy to help!

[@ziwasafira418]

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

[@terminatorougtifv]

Thank you. Articulate and informative.

[@gavind.7918]

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

[@saminkamal3670]

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

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Honestly, 5/5 stars math teacher.

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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....

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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🙏

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[@-clipz-]

God bless

[@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!

[@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

[@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!

[@guinereyes2463]

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

[@peachycsc7905]

this video helped me in my distance learning. thank you!

[@Doolin.S]

You literally just saved my homework grade😅

[@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...

[@ChrisS-rp7yo]

Thanks helpful a on all my tests

[@7wolfgaming710]

great video explains a point clearly

[@ryderleitch2125]

only if everyone had a teacher like you

[@ran29120]

That make sense! 👏 Bless this teacher🙏

[@theDjwan]

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

[@skullcrusher701]

I have a test tomorrow and it was dire that I find a video like this to aid me! Thanks!

[@brianmclogan]

skullcrusher701 very welcome! how did you do?

[@skullcrusher701]

93! The part of the test that this video was over, I got correct.
Btw my teacher took a while to grade so I had to wait to comment.

[@_Gontse]

Where have you been all my life ??? Thank you so much , you elaborate so much clearer than my teacher and I actually understand my homework now.

[@brianmclogan]

just here making videos! glad you found me and I am able to help you out!

[@superrexer6816]

You explained this a million times better than my online Algebra 2 course thanks man

[@brianmclogan]

happy to be able to help

[@maccleary9576]

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

[@tokenking6]

Thanks for all the great info!

[@sarahhill7140]

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

[@ChrisS-rp7yo]

Thank really helpful got a on all my tests

[@musical_costumer7976]

Took me a minute to understand, but now I do!! Thank you!

[@iviwemndi176]

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

[@nehemiahprado4103]

Best college algebra video... helped out alot

[@earltagapolot9559]

omg i wish i had you as my math teacher

[@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

[@themostmlgjellybean607]

Wow. It is amazing how this 9 minutes is more effective then 5 classes of algebra. Thank you

[@matthewwood8269]

THANKS SO MUCH, this has helped me so much on my maths homework. I couldn't have done done it without this video.

[@brianmclogan]

Happy to be able to help you out!

[@koseakalema2290]

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

[@hawkie2216]

Your the only person I could understand.

[@precioussiete1391]

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

[@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💯

[@sevalkaya74]

You could’ve also plugged in 4th term or 10th to solve for a sub 1. Then using a sub 1 and common ratio you could simply find out 14th term. I def understand the pressure but this how I would do. Thanks for the transparency!

[@tanghulu_prince]

how?

[@analisantos3207]

@Brian McLogan Thank you for your video!
I teach Maths and currently have a student that I am preparing for a Medicine exam. When teaching her about geometric progressions, she was quite puzzled about the possibility of negative common ratios, because she couldn't picture a real life example of an application for these. My training is fundamental, not applied Maths, so I am also having a hard time coming up with an example. Do you have any ideas? Thank you in advance.

[@nathanharris8262]

Wow you have helped me so much with pre-calc. Thank you!

[@JohannesMosie]

Thank because I'm writing an exam tomorrow

[@zhnkbr]

is there a reason for not using simultaneous equations ?

[@joanamaylumongsud3390]

you're an amazing teacher I do learn after watching your video . You help a lot. I hope i'll be able to answer for the Math QUIZ :D

[@brianmclogan]

just happy to be able to help you out!

[@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?

[@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=

[@kcmouli8766]

U are very active sir

[@baileyhonaker5976]

You teaching me this. Has helped me :) my teacher won't! So i rely on you!!

[@jessicamiriam2897]

THIS GUY IS BRILLIANT

[@emilialuoma3398]

Thanks, you just saved me from my mental breakdown

[@brianmclogan]

Boom!

[@danieldrewbustillos3380]

How do you find the 1st term sir?

[@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?

[@asharibimran5645]

great explanation!!u nailed it,but plz can u explain what is geometric sequence???

[@brianmclogan]

basically a sequence of numbers that have a common ratio between the terms

[@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

[@doingboing4608]

Thank you Brian

[@brianmclogan]

You are very welcome

[@jeremyclark9697]

This was very helpful

[@wengramos]

Had a similar problem like this on my math homework. Thanks so much for this, it really helped a lot!

[@aniki.]

Legendary, thank you!

[@no-jp9oe]

You just saved my final grade! Thank you!

[@ayaanmumtaz2007]

Thank you sir , it helped me a lot

[@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!

[@stvndnh1071]

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

[@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.

[@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?

[@jasmineortiz1050]

you inspire me to be a math teacher

[@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

[@jaredtreat2729]

thank you very much

[@jasmineortiz1050]

im flying through my work thanks bro

[@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

[@miamiau-p7n]

this made me learn more than i learned in a week lol

[@jasminelie1600]

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

[@thorstambaugh1520]

What if the progression is formulaic with 2 variables?

[@CoulRanch]

Who else is here watching this in 2097?

[@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

[@lucatmylife8075]

Your videos are really helpful thank you !

[@brianmclogan]

you are very welcome!

[@oscarromerojr]

Thank you so much very helpful ❤️

[@sarahmateo9043]

The BEST!!👍👍👌

[@jessielyon]

Thank you so much. That was so helpful!

[@jessielyon]

I'm doing this in 9th grade in advanced algebra 2.

[@brianmclogan]

good for you, keep up the hard work!