The sum of the first n terms of a geometric progression (GP) can be found using the formula:

S_n​ = [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

S_5​ = [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 S_n​ = [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.