How to Find Sum of First n Terms of GP?
Last Updated :
05 Mar, 2024
The sum of the first n terms of a geometric progression (GP) can be found using the formula:
Sn​ = [Tex]{a(\frac{r^n-1}{r-1})}[/Tex]​
Here, a is the first term of the GP, r is the common ratio, and n represents the number of terms.
To calculate the sum of the first 5 terms of a geometric progression with the first term a = 2 and common ratio r = 3
S5​ = [Tex]\bold{2(\frac{3^5-1}{3-1})}[/Tex] = 242
After evaluating the expression, the sum of the first 5 terms of this geometric progression is 242.
This formula efficiently accounts for the cumulative contribution of each term in the progression, providing a valuable tool in mathematical calculations and real-world scenarios involving geometric progressions. Calculating the sum of a geometric progression is a fundamental task in mathematics, widely applicable in fields like finance, physics, and computer science. The formula Sn​ = [Tex]{a(\frac{r^n-1}{r-1})}[/Tex] simplifies this process, offering a concise way to determine the cumulative value of the first n terms.
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