What Is Geometric Series And Its Example?
What is Geometric Series and its Example?
Deret Geometri, or geometric series, is a series of numbers in which each term is multiplied by a common ratio to get the next term. It is usually represented by a sequence of numbers that follows a certain pattern. In mathematics, a geometric series is a way of expressing an infinite sum of terms where each term is the product of the previous term and a constant factor. It is a type of series that is used to solve many mathematical problems.
How to Find the Sum of a Geometric Series?
The sum of a geometric series can be found by using the formula: S = a + ar + ar2 + ar3 + . . . + arn-1 where a is the first term of the series and r is the common ratio. The sum of the geometric series can be written as S = a (1 - rn) / (1 - r).
What is an Example of a Geometric Series?
An example of a geometric series is the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Here, the first term is 1 and the common ratio is 2. We can calculate the sum of the geometric series using the formula S = a (1 - rn) / (1 - r). Therefore, the sum of this series is 2046.
What is the Formula for Geometric Series?
The formula for geometric series is S = a + ar + ar2 + ar3 + . . . + arn-1 where a is the first term of the series and r is the common ratio. The sum of the geometric series can be written as S = a (1 - rn) / (1 - r).
What is Geometric Progression?
Geometric progression is a sequence of numbers in which each term is multiplied by a common ratio to get the next term. It is a type of series that is used to solve many mathematical problems. The sum of a geometric series can be found using the formula S = a (1 - rn) / (1 - r).
What is an Example of a Geometric Progression?
An example of a geometric progression is the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Here, the first term is 1 and the common ratio is 2.
What is the Difference Between Geometric Series and Geometric Progression?
The main difference between geometric series and geometric progression is that a geometric series is a type of series while a geometric progression is a type of sequence. A geometric series is a way of expressing an infinite sum of terms where each term is the product of the previous term and a constant factor. A geometric progression is a sequence of numbers in which each term is multiplied by a common ratio to get the next term.
What is the Formula for the nth Term of a Geometric Series?
The formula for the nth term of a geometric series is a (rn-1). Here, a is the first term of the series and r is the common ratio.
Conclusion
Deret Geometri, or geometric series, is a series of numbers in which each term is multiplied by a common ratio to get the next term. It is usually represented by a sequence of numbers that follows a certain pattern. The formula for geometric series is S = a + ar + ar2 + ar3 + . . . + arn-1 where a is the first term of the series and r is the common ratio. Geometric progression is a sequence of numbers in which each term is multiplied by a common ratio to get the next term. The formula for the nth term of a geometric series is a (rn-1).
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