The Sum of Finite Geometric Series Calculator helps users find the total sum of a finite geometric series. A geometric series is a sequence of numbers where each term is found by multiplying the previous term by a fixed, non-zero number called the common ratio. This calculator is particularly useful for students, educators, and professionals who need to perform these calculations efficiently.
Formula of Sum of Finite Geometric Series Calculator
The formula used by the Sum of Finite Geometric Series Calculator is:
where:
- S_n is the sum of the series
- a_1 is the first term of the series
- r is the common ratio between successive terms (the number you multiply by to get from one term to the next)
- n is the number of terms in the series
This formula provides a straightforward method to compute the sum without manually adding each term.
Common Terms Table
Here is a table of common values and their corresponding results for quick reference:
| First Term (a_1) | Common Ratio (r) | Number of Terms (n) | Sum (S_n) |
|---|---|---|---|
| 1 | 2 | 5 | 31 |
| 3 | 0.5 | 4 | 5.25 |
| 2 | -1 | 3 | 1 |
| 5 | 3 | 4 | 200 |
| 10 | 0.1 | 6 | 11.1111 |
Example of Sum of Finite Geometric Series Calculator
Let’s go through an example to understand how the Sum of Finite Geometric Series Calculator works.
Example:
Find the sum of the first 6 terms of a geometric series where the first term (a_1) is 2 and the common ratio (r) is 3.
Using the formula:
S_n = a_1 * (1 – r^n) / (1 – r)
Substitute the given values:
S_6 = 2 * (-728) / (-2)
S_6 = 2 * 364 = 728
So, the sum of the first 6 terms is 728.
Most Common FAQs
A geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio.
The common ratio (r) can be found by dividing any term in the series by the previous term. For example, if the second term is 6 and the first term is 2, then the common ratio is 6 / 2 = 3.
Yes, the common ratio in a geometric series can be negative. This will cause the terms to alternate in sign.