How many TOTAL people would there be by generation 9?

Ajouté : 2026-05-20

[00:00:00]How many total people will there be by generation nine? And you also mentioned that Google isn't helping. Well, let's have a look. Let's try to figure out a pattern. So, here is the deal. Imagine right here this is our first person. So, this is the first generation. And the assumption is that each generation will produce like two people. So, the next generation is that we will have one here and then two here.

[00:00:28]So, that's generation two. So, notice that right now we have a total of three people. And then assuming each person give us like one, two, and then one, two like this.

[00:00:46]So, by generation three, we have a total of 1 + 2 + 4, which is seven. And this right here keeps on going forever. And we'll get so many people by generation nine. And the question is how many people are we going to have all together right here?

[00:01:06]Okay. So, notice that each person will produce two. And we have that pattern.

[00:01:12]So, we are dealing with a power of two.

[00:01:15]And assuming if this is the first time we are seeing it, I would like to show you how we can figure it out. And to do so, you want to start with some small numbers and try to see if you can figure out a pattern.

[00:01:27]generation And then we have the total number of people. So, let's say in the first generation, it's just one person. Okay? And then second generation we have a total of 1 + 2.

[00:01:47]So, that's three. And then third generation we have a total of 1 + 2 + 4.

[00:01:56]And that is the same as seven. And the fourth generation this will just be 1 + 2 + 4 + 8 because each of these will give you two more.

[00:02:09]So, you double that. So, that's eight.

[00:02:11]Add them up, you get 15 and so on so on so on.

[00:02:16]What we want to get to is nine.

[00:02:19]So, by generation nine, we are looking at 1 + 2 + 4 + 8 + dot dot dot up to uh last number here.

[00:02:30]What is it though?

[00:02:31]Well, let's go back to the the previous and try to see if we can figure out a pattern.

[00:02:36]This number is eight. Like that's the last number. But remember to get this number, each time we just multiply by two. This is the same as 2 * 2 * 2, which is 2 to the third power.

[00:02:48]Let me write it down right here.

[00:02:54]And then this right here, in fact, is just 2 to the second power. And of course, this right here is just 2 to the first power. And this right here by default is just 2 to the zeroth power. In fact, you didn't multiply by two at all. That's where you begin with.

[00:03:13]So, when it's at four this is 2 to the third power.

[00:03:19]When it's three, it's 2 to the second.

[00:03:21]When you want to get to nine, this last number will be 2 to the eighth power.

[00:03:27]And you can work it out by I will just keep it like that. Because what we want to do next is to figure out that pattern for the answers.

[00:03:36]one three seven 15 and so on so on so on. What's this right here?

[00:03:44]In fact, when you're adding 1 + 2 + 4 + dot dot dot up to the last one right here the answer is just 2 to the ninth power minus one.

[00:03:56]Why? Because this 15 is what?

[00:03:58]This 15 you can look at this as 2 to the fourth power, which is 16, minus one.

[00:04:04]The seven, it's the same as 2 to the third power minus one. Likewise, the three is the same as 2 to the second minus one.

[00:04:13]And of course, this right here is the same as 2 to the first minus one.

[00:04:17]So, all this will give you 2 to the ninth power minus one.

[00:04:23]Okay.

[00:04:24]2 to the tenth power is 1024. So, 2 to the ninth power is equal to 512. And then minus one, that will give you a total of 511.

[00:04:37]So, that will be a lot of people right here.