In this video we'll do a couple examples from delta math uh distinguished arithmetic versus geometric sequences so we're going to look at the sequence they give you and determine if it's geometric or arithmetic so we gotta look does have a common difference or a common ratio.
Well 20 minus 4 is 16 and 100 minus 20 is 80. so we quickly see that this is not a common difference so now does have a common ratio 100 divided by 20 that's 5. oh 20 divided by 4 is 5. so we can see that this is a geometric sequence and it has a common ratio.
And the common ratio is 5 because we get 100 over 20 reduces to 5 over 1 or 20 divided by 4 reduces to 5 over 1. and then that is what we multiply by to generate the next term so the next term this sequence would be 500 100 times 5 is 500. submit the answer see if we get the.
Check mark and we do and it shows us the whole process here's our next problem 3 12 21 so 12 minus 3 is 9 21 minus 12 is 9. so this one has a common difference so we say it's arithmetic sequence common difference is equal to.
9. look at our next sequence 125 25 5 so this sequence is decreasing so let's look does it have a common difference well 25 minus 125 is negative 100 and then 5 minus 25 is negative 20. so it does not have a common difference now does it have a common ratio well.
25 divided by 125 reduces to 1 over 5. 5 divided by 25 reduces to one over five so this is a geometric sequence has a common ratio which is one over five now be careful sometimes students think of this as divide by five but remember the common ratio is what are we multiplying by each term.
To get the next term so in other words our next term would be 5 times 1 5th gets us to 1. and i know a lot of you think it's 5 divided by 5 which gets you to 1 as well but again when we talk about the common ratios what is that multiplier so one-fifth is our answer and we enter it.
There we go look at one more sequence 2 11 20. all right so does it have a common difference let's see 20 minus 11 is 9. 11 minus 2 is 9. oh so they're just adding 9 each time so this is an arithmetic sequence it has a common difference in that difference value is oops nine.