WEBVTT 00:00:00.628 --> 00:00:01.835 - [Voiceover] What I want to in this video 00:00:01.835 --> 00:00:05.202 is get some practice figuring out patterns and numbers. 00:00:05.202 --> 00:00:07.524 In particular, patterns that take us from 00:00:07.524 --> 00:00:10.903 one number to a next number in a sequence. 00:00:10.903 --> 00:00:13.596 So over here, in this magenta color, 00:00:13.596 --> 00:00:18.263 I go from 4 to 25 to 46 to 67. 00:00:18.263 --> 00:00:20.393 So what's the pattern here? 00:00:20.393 --> 00:00:22.831 How did I get from 4 to 25 00:00:22.831 --> 00:00:25.502 and can I get the same way from 25 to 46 00:00:25.502 --> 00:00:30.308 and 46 to 67, and I could just keep going on and on and on? 00:00:30.308 --> 00:00:31.887 Well there's a couple of ways to think about it. 00:00:31.887 --> 00:00:33.986 When I see 4 and 25, let's see, 00:00:33.986 --> 00:00:38.026 25 isn't an obvious multiple of 4. 00:00:38.026 --> 00:00:43.026 Another way to go from 4 to 25, I could add 21. 00:00:43.041 --> 00:00:48.041 Let's see, if I add 21, 4 plus 21 is 25. 00:00:48.196 --> 00:00:51.052 If I were to go from 25 to 46, 00:00:51.052 --> 00:00:53.025 well I could just add 21 again. 00:00:53.025 --> 00:00:55.835 It looks like to go from one number to the next 00:00:55.835 --> 00:00:57.483 I'm just adding. 00:00:57.483 --> 00:00:59.573 I wrote 12 by accident, 21. 00:00:59.573 --> 00:01:02.684 I'm just adding 21 over and over again. 00:01:02.684 --> 00:01:07.166 That's going to be 46 plus 21 is 67. 00:01:07.166 --> 00:01:11.159 And if I were to keep going, if I add 21 00:01:11.159 --> 00:01:13.110 I'm going to get to 89. 00:01:13.110 --> 00:01:18.110 If I add 21 to that I'm going to get 110, 00:01:20.865 --> 00:01:22.955 and I could keep going and going and going. 00:01:22.955 --> 00:01:27.157 I could just keep adding 21 over and over again. 00:01:27.157 --> 00:01:31.522 The pattern here is I'm adding 21. 00:01:31.522 --> 00:01:34.471 Now what about over here, in green? 00:01:34.471 --> 00:01:36.607 When I look at it at first, it's tempting to say, 00:01:36.607 --> 00:01:40.276 3 plus 3 is 6. 00:01:40.276 --> 00:01:43.480 But then I'm not adding 3 anymore to get 00:01:43.480 --> 00:01:46.290 from 6 to 12, I'm adding 6. 00:01:46.290 --> 00:01:48.147 And then to get from 12 to 24, 00:01:48.147 --> 00:01:51.096 I'm not adding 6 anymore, I added 12. 00:01:51.096 --> 00:01:54.463 So every time I'm adding twice as much. 00:01:54.463 --> 00:01:58.389 But maybe an easier pattern might be, 00:01:58.389 --> 00:01:59.884 another way to go from 3 to 6, 00:01:59.884 --> 00:02:03.738 isn't to add 3, but to multiply it by 2. 00:02:03.738 --> 00:02:06.501 So I multiply by 2 to go from 3 to 6, 00:02:06.501 --> 00:02:10.030 and if I multiply by 2 again, I go from 6 to 12. 00:02:10.030 --> 00:02:11.818 6 times 2 is 12. 00:02:11.818 --> 00:02:14.929 If I multiply by 2 again, I'll go to 24. 00:02:14.929 --> 00:02:19.457 2 times 12 is 24 and I could keep going on and on and on. 00:02:19.457 --> 00:02:23.520 2 times 24 is 48, 96, I could go on and on and on. 00:02:23.520 --> 00:02:26.353 The pattern here, it's not adding a fixed amount, 00:02:26.353 --> 00:02:30.927 it's multiplying each number by a certain amount, 00:02:30.927 --> 00:02:33.760 by 2 in this case, to get the next number. 00:02:33.760 --> 00:02:38.102 So 3 times 2 is 6, 6 times 2 is 12, 12 times 2 is 24. 00:02:38.102 --> 00:02:40.076 Alright, now let's look at this last one. 00:02:40.076 --> 00:02:42.908 The first two terms here are the same, 3 and 6. 00:02:42.908 --> 00:02:46.117 The first two numbers here. 00:02:46.117 --> 00:02:47.833 I could say, maybe this is times 2, 00:02:47.833 --> 00:02:51.223 but then to go from 6 to 9, I'm not multiplying by 2. 00:02:51.223 --> 00:02:53.429 But maybe I am just adding 3 here. 00:02:53.429 --> 00:02:55.937 So 3 to 6, I just added 3. 00:02:55.937 --> 00:02:59.327 Then 6 to 9, I add 3 again, 00:02:59.327 --> 00:03:02.276 and then 9 to 12, I add 3 again. 00:03:02.276 --> 00:03:03.506 So this one actually does look like 00:03:03.506 --> 00:03:06.432 I'm just adding 3 every time. 00:03:06.432 --> 00:03:09.633 The whole point here is to see, is there something I can do, 00:03:09.633 --> 00:03:12.142 can I do the same something over and over again 00:03:12.142 --> 00:03:13.814 to get from one number to 00:03:13.814 --> 00:03:16.786 the next number in a sequence like this? 00:03:16.786 --> 00:03:18.637 What you want to make sure is even if you think you know 00:03:18.637 --> 00:03:20.480 how to go from the first number to the second number, 00:03:20.480 --> 00:03:22.175 you've got to make sure that that same way works 00:03:22.175 --> 00:03:24.961 to go from the second number to the third number, 00:03:24.961 --> 00:03:27.074 and the third number to the fourth number. 00:03:27.074 --> 00:03:28.258 But here we figured it out. 00:03:28.258 --> 00:03:31.323 In this first set of numbers, we just add 21 every time. 00:03:31.323 --> 00:03:33.274 This one we multiply by 2 every time. 00:03:33.274 --> 00:03:37.083 This one we add 3 every time.