sum of a gP calculator

About Sum of a GP Calculator?

The sum of n terms of a geometric progression (GP) is the total value obtained by adding up the first n terms of the sequence. In a GP, each term is found by multiplying the previous term by a constant ratio called the common ratio (r). The formula to calculate the sum of n terms of a GP is given by:

Sn = (a * (r^n - 1)) / (r - 1),

where Sn represents the sum, a is the first term, r is the common ratio, and n is the number of terms. This formula allows us to determine the sum of any number of terms in a geometric sequence efficiently. MathCrave sum of a GP calculator finds out the sum of n terms of geometric progression with detailed step by step worksheets.

Understanding Sum of a GP, and How it Works

To calculate sum of a n terms of a geometric progression, hen the n-term, first term, and ratio are given, follow these steps:

• Determine the common ratio (r) by dividing the n-term by the first term.

• Use the formula Sn = (a * (r^n - 1)) / (r - 1) to calculate the sum, where Sn is the sum, a is the first term, r is the common ratio, and n is the number of terms.

Worked Example of Sum of a GP

Let's solve an example to find the sum of n terms of a geometric progression.

Find the sum of the first 5 terms of the geometric progression with the first term (a) as 2 and the common ratio (r) as 3.

Solution

• Step 1: Determine the common ratio

• (r) = 3.

• Step 2: Use the formula

• Sn = (a * (r^n - 1)) / (r - 1) to calculate the sum.

• Substituting the given values, we get

• Sn = (2 * (3^5 - 1)) / (3 - 1).

• Simplifying further,

• Sn = (2 * (243 - 1)) / 2 = 242.

• Therefore, the sum of the first 5 terms of the geometric progression is 242.