Patterns in arithmetic
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- [Voiceover] What I want to in this video is get some practice figuring out patterns and numbers. In particular, patterns that take us from one number to a next number in a sequence. So over here, in this magenta color, I go from 4 to 25 to 46 to 67. So what's the pattern here? How did I get from 4 to 25 and can I get the same way from 25 to 46 and 46 to 67, and I could just keep going on and on and on? Well there's a couple of ways to think about it. When I see 4 and 25, let's see, 25 isn't an obvious multiple of 4. Another way to go from 4 to 25, I could add 21. Let's see, if I add 21, 4 plus 21 is 25. If I were to go from 25 to 46, well I could just add 21 again. It looks like to go from one number to the next I'm just adding. I wrote 12 by accident, 21. I'm just adding 21 over and over again. That's going to be 46 plus 21 is 67. And if I were to keep going, if I add 21 I'm going to get to 89. If I add 21 to that I'm going to get 110, and I could keep going and going and going. I could just keep adding 21 over and over again. The pattern here is I'm adding 21. Now what about over here, in green? When I look at it at first, it's tempting to say, 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 to 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, another way to go from 3 to 6, isn't to add 3, but to multiply it by 2. So I multiply by 2 to go from 3 to 6, and if I multiply by 2 again, I go from 6 to 12. 6 times 2 is 12. If I multiply 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. The pattern here, it's not adding a fixed amount, it's multiplying each number 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. Alright, now let's look at this last one. The first two terms here are the same, 3 and 6. The first two numbers here. I could say, 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. The whole point here is to see, is there something I can do, can I do the same something over and over again to get from one number to the next number in a sequence like this? 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've 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.