Geometric Progression for Dummies
noun
What does Geometric Progression really mean?
Geometric Progression:
Hey there! So, today we're going to talk about this mathematical concept called "geometric progression." Now, I know the words might sound a bit intimidating, but don't worry, I'm here to break it down for you in the simplest way possible, okay?
Imagine you have a sequence of numbers, like 1, 2, 4, 8, 16... What do you notice about these numbers? Well, if you look closely, each number is obtained by multiplying the previous number by the same value, which is 2 in this case. So, if we started with 1 and we multiply it by 2, we get 2. Then, we multiply 2 by 2 again and we get 4. We keep doing this, multiplying by 2 each time, and that's how we get the other numbers in the sequence.
This is basically the essence of geometric progression. It's a sequence of numbers where each term is found by multiplying the previous term by a fixed value called the "common ratio." In our example, the common ratio is 2 because we always multiplied by 2. The idea is that the sequence keeps growing or shrinking in a predictable way.
Now, geometric progression can have different kinds of behavior. For example, if the common ratio is a value greater than 1, like 2 in our sequence, then the terms will keep getting bigger and bigger as we go along. On the other hand, if the common ratio is a value between 0 and 1, like ½, the terms will actually get smaller and smaller as we move forward. It's like we're zooming in or zooming out of a picture.
That's not all though! Geometric progression can also have a sum. So let's say we want to calculate the sum of the terms in a geometric progression. There's actually a formula for that! It involves the first term, the common ratio, and the number of terms in the progression. The formula may look a bit complex at first, but it's just a way for us to quickly add up all the terms without having to do it one by one.
So, to sum it all up, geometric progression is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed value called the common ratio. It can either grow or shrink depending on whether the common ratio is greater than 1 or between 0 and 1. And we can also calculate the sum of the terms in a geometric progression using a special formula.
I hope that makes sense to you! If you have any more questions, feel free to ask.
Hey there! So, today we're going to talk about this mathematical concept called "geometric progression." Now, I know the words might sound a bit intimidating, but don't worry, I'm here to break it down for you in the simplest way possible, okay?
Imagine you have a sequence of numbers, like 1, 2, 4, 8, 16... What do you notice about these numbers? Well, if you look closely, each number is obtained by multiplying the previous number by the same value, which is 2 in this case. So, if we started with 1 and we multiply it by 2, we get 2. Then, we multiply 2 by 2 again and we get 4. We keep doing this, multiplying by 2 each time, and that's how we get the other numbers in the sequence.
This is basically the essence of geometric progression. It's a sequence of numbers where each term is found by multiplying the previous term by a fixed value called the "common ratio." In our example, the common ratio is 2 because we always multiplied by 2. The idea is that the sequence keeps growing or shrinking in a predictable way.
Now, geometric progression can have different kinds of behavior. For example, if the common ratio is a value greater than 1, like 2 in our sequence, then the terms will keep getting bigger and bigger as we go along. On the other hand, if the common ratio is a value between 0 and 1, like ½, the terms will actually get smaller and smaller as we move forward. It's like we're zooming in or zooming out of a picture.
That's not all though! Geometric progression can also have a sum. So let's say we want to calculate the sum of the terms in a geometric progression. There's actually a formula for that! It involves the first term, the common ratio, and the number of terms in the progression. The formula may look a bit complex at first, but it's just a way for us to quickly add up all the terms without having to do it one by one.
So, to sum it all up, geometric progression is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed value called the common ratio. It can either grow or shrink depending on whether the common ratio is greater than 1 or between 0 and 1. And we can also calculate the sum of the terms in a geometric progression using a special formula.
I hope that makes sense to you! If you have any more questions, feel free to ask.
Revised and Fact checked by Megan Brown on 2023-10-29 07:01:37
Geometric Progression In a sentece
Learn how to use Geometric Progression inside a sentece
- In a geometric progression, if the first term is 2 and the common ratio is 3, then the sequence would be 2, 6, 18, 54, 162...
- Let's say you have 5 balloons and each balloon is 2 times bigger than the previous one. The sizes of the balloons would be 5 cm, 10 cm, 20 cm, 40 cm, 80 cm... This is an example of a geometric progression.
- Suppose you have a bank account with an initial deposit of $100 and the interest rate is 10%. Each year, the amount in the account would increase by 10% compared to the previous year. After the first year, you would have $110, after the second year $121, after the third year $133.10, and so on. This is an example of a geometric progression.
- If you start with 1 and keep multiplying by 2, the sequence would be 1, 2, 4, 8, 16, 32... This is an example of a geometric progression.
- Imagine you have a population of rabbits. If each pair of rabbits produces 3 new pairs of rabbits every month, then the number of rabbits in each month would be 2, 6, 18, 54, 162, and so on. This is an example of a geometric progression.
Geometric Progression Hypernyms
Words that are more generic than the original word.
Geometric Progression Category
The domain category to which the original word belongs.