Geometric Sequences

[@prod.bychop]

bros clutchin b4 my exam thnx so much fam!

[@sueregal6317]

Very helpful!!! :) you've got a way to explain things

[@enighaty3342]

Why did you +and - the root 9 but you never did plus or minus when you rooted anything else

[@temidayofalomo991]

Great Video!

[@josephisrael8959]

has this been moved down to the 9-1 gcse system

[@MaxStrongman]

I think it has been moved down but you should double check

[@CorruptTM-g3o]

@@MaxStrongmanyeah it came today in paper 3 as a five marker for edexcel higher gcse

[@thegoldengamer9315]

​​@@CorruptTM-g3o some stupid question

[@MaxStrongman]

@@CorruptTM-g3o i didnt quite get it right : (

[@CorruptTM-g3o]

@@MaxStrongman yeah neither did i , as a matter of fact , i didnt even know this topic could come in , hopefully we get working out marks anyway

[@shiv8060]

studypug this video will help more than u ever will

[@shockedchrispcats33]

studypug sucks and is a scam

[@MaxStrongman]

great video

[@enighaty3342]

Need HELP

[@fluffyalien5174]

What if there was U3=32 , U6=1/2 , and we must find the general term ?? :(

[@totallyrandomnobody3920]

I hope you're not dead yet as you read the answer for your question. Given that U3=32 and U6=1/2 We're basically going to prove this by aligning our equations to each other by using division, why do we use division in terms of Geometric? Simple, because it uses the operations of Multiplication and Division! Let 32 represent U3 and Let 1/2 represent U6 Remember the formula for the Geometric sequence? Which is: Un= U1 times R^ n-1 Yep, plug it all in U3= U1 times R^3-1 / 32=u1 times R^2 U6= U1 times R^6-1 / 1/2=u1 times R^5 Divide them both side by side as if they were fractions 32 divided by 1/2 would become 1/32 times 1/2, because fraction rules and whole numbers are hated and put in the denominator, which is basically 1/32 times 1/2 which becomes 1/64 now the rest of the operations looks like: 1/64 = U1 and r^2 / U1 and r^5 Now the U1 cancels each other out because numerator and denominator thingy, and r^2 divided by r^5 would become r^5-2 which is equal to r^3 because exponent rules. Now the equation looks like 1/64 = r^3 Now in order to cancel the 3 above the r, we need to find the cube root which basically is square root with 3 outside, because you need 3 3rd root of 1/64 = 3rd root of r^3 cancels each other's 3, now we're left with r 3rd root of 1/64 = r Now what is the 3rd root of 1 over 64? simple! find common factors which are 3 clones of each other Now we're going to focus on 64 and mind its numerator later, what are the numbers that multiplies to 64? 64= 8 times 8. and you can get both 8s by? 8= 4 times 2, and you can get 4 by what? 4= 2 times 2 See the 2s? yep you have 3 of them! and another 3 of 2! Now that's basically 2 times 2 which is equals to 4 therefore your equation looks like 1/4 = r Don't forget that is 1/64 earlier, we'll just plug it in Now how about its U1? Simple, since you have your ratio, now you can prove it! Let's try injecting it into the equation of U3 32 = U1 times (1/4) ^ 2 The ^ 2 of 1/4 is basically 1/4 times 1/4 which is equal to 1/16, Now it looks like 32 = U1 times 1/16 Since 16 is in the denominator, you can basically multiply it by the other side since the fraction rules say so, so it is now 32 times 16 = U1 32 x 16 = 512 Now it looks like 512 = a1 Now we have it all, U1= 512 and R = 1/4 Now it's up to you to prove this since you've read this far I hope you're living a great life after 2 years; I'm basically reviewing every math video now in summer because I'm trying to get to my Dream College. I am not Indian nor Chinese, but I can prove a fight if needed to lol

[@GhazanMunsif]

@@totallyrandomnobody3920 damn bruh