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# Finding patterns in numbers

CCSS.Math:

## Video transcript

what I want to do in this video is get some practice figuring out patterns in numbers and in particular patterns that take us from one number to a next number in a sequence so 4 over here over here in this magenta color I go from four to twenty five to forty six to sixty seven so what's what's the pattern here what how did I get from four to twenty five and can I get the same way from twenty five to forty six and forty six to sixty seven and could I just keep going on and on and on well there's a couple of ways to think about when I see four and twenty five let's see 25 isn't an obvious multiple of four let's see another way to go from four to 25 I could add 21 so let's see if I add 21 4 plus 21 is 25 let's see if I were to to go from 25 to 46 well I could just add 21 again so it looks like to go from one number to the next I'm just adding I'm just I wrote 12 by exit 21 I'm just adding 21 over and over again so that's going to be 46 plus 21 is 67 and if I were to keep going if I were to keep going let's see if I had 21 I'm going to get 289 if I had 21 to that I'm going to get 100 and I'm just going to get 110 and I could keep going and going and going I could just keep adding 21 over and over again so the pattern here is I am adding 21 now what about over here in green well when I look at it at first it's tempting to say okay 3 plus 3 is 6 but then I'm not adding 3 anymore to get from 6 to 12 I'm adding 6 and then I get from 12 to 24 I'm not adding 6 anymore I added 12 so every time I'm adding twice as much but maybe an easier pattern might be an easier pattern might be another way to go from 3 to 6 isn't to add 3 but 2 multiplied by 2 so I'm multiplied by 2 to go from 3 to 6 and if I multiply by 2 again I'll go from 6 to 12 6 times 2 is 12 and if I multiply it by 2 again I'll go to 24 2 times 12 is 24 and I could keep going on and on and on 2 times 24 is 48 96 I could go on and on and on so the pattern here it's not adding us fixed amount it's multiplying each each number by a by a certain amount by 2 in this case to get the next number so 3 times 2 is 6 6 times 2 is 12 12 times 2 is 24 all right now let's look at this last one so the first two terms you're the same 3 & 6 the first two numbers here but to go so I could say well maybe this is times 2 but then to go from 6 to 9 I'm not multiplying by 2 but maybe I am just adding 3 here so 3 to 6 I just added 3 then 6 to 9 I add 3 again and then 9 to 12 I add 3 again so this one actually does look like I'm just adding 3 every time so the whole point here is to see well is there something I can do the same can do the same something over and over again forget from one number to the next number in a sequence like this and what you want to make sure is even if you think you know how to go from the first number to the second number you got to make sure that that same way works to go from the second number to the third number and the third number to the fourth number but here we figured it out in this first set of numbers we just add 21 every time this one we multiply by 2 every time this one we add 3 every time