in this video I will be talking about the difference between finite and infinite geometric sequence so let us differentiate the two the finite geometric sequence and the infinite geometric sequence so let us divide this and let's compare so let me show you a geometric sequence so this is an example of geometric sequence 2 4 8 16 32 64 and 128 this is because we have we multiply two or each term to get the next term so 2 times 2 is 4 4 times 2 is 8 8 times 2 16 16 times 2 32 32 times 2 64 and 64 times to 120 that's why it's a geometric sequence because we have a common number multiplied to each term and another one we have this sequence this is also a geometric sequence so the same terms except that we have a comma and the three dots after 100 day and that makes it infinite geometric sequence so what does it mean by that so both have common ratio so of course the common ratio since its times 2 for each term it will be R equals 2 where there are means ratio or the common ratio and then they both have a first trip or the a sub 1 so the a sub 1 or the first time we see qualitative or the finance geometric sequence and a sub 1 it was also - for the infinite geometric sequence we had they both have first term and a sub n which is the last term the last term for this which is that a sub 7 so we'll just make it general the last term is 128 for finite geometric sequence in a last term for infinite geometric sequence or the a sub n is none there's no last term for this as you can see after 128 is comma and 3 does it means it continues infinitely so it will keep on multiplying 2 and tear and so once there's no ending of multiplying 2 where and in the finite you will see geometric sequence it will just end up to 128 but still it is still geometric sequence because it follows the same uniform pattern it's x do while infinite geometric sequence it it follows the pattern infinitely by multiplying 2 sometimes the infinite geometric sequences like this so we have 3 dots and a comma before the two as well as three dots and a comma Custer 108 so what does it mean by this it means there is no first term so in the previous one we have a first-term to left here we have we don't have a first term but why did we start from to it there's no first term it this is just this is an infinite geometric sequence where it is just showing a part of the infinite geometric sequence so it's just a portion from 2 to 128 but actually there are still numbers before too so you can have you can divide by 2 to know what's before the to see it means before the 2 is 1 and before one is one happened and so on so those are the the terms where we cannot say that they are the first term because they are infinitely many number for to and there are infinitely many number after 120 and also there is no last term for this infinite geometric sequence and so that's it so that's the difference between finite and infinite geometric sequence thanks for watching and I hope you have learned from this video please support my channel by pressing the subscribe button and also write the math topics you want to learn in the comment section