Sum of a GP Calculator

calculator, Sum of n terms of a GP

**Sum of n terms of a GP.** When the **first**, **ratio**, ** nth ** terms are given.\[S_n=\frac{a(r^n - 1)}{r - 1}\]

Sun of a GP calculator calculates the sum of n terms of a geometric progression (sum of a GP) with detailed worksheets.

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.

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.

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

**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.

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