Sum Of Terms In A Geometric Progression

Introduction

Geometric Progression (GP) is a sequence of numbers in which each term is obtained by multiplying the previous term by a constant ratio. In this article, we will discuss an iterative approach to finding the sum of terms in a Geometric Progression. We will cover the understanding of Geometric Progression, the approach to finding the sum of terms, and provide a step-by-step solution with sample code.

Understanding Geometric Progression

A Geometric Progression is a sequence of numbers in which each term, starting from the second term, is obtained by multiplying the previous term by a fixed ratio called the common ratio (r). The general form of a Geometric Progression is a, ar, ar^2, ar^3, ..., where 'a' is the first term and 'r' is the common ratio.

Approach

To find the sum of terms in a Geometric Progression, we can use an iterative approach. Starting from the first term (a), we can multiply the term by the common ratio (r) and sum up the terms for the desired number of iterations. By iteratively applying the common ratio and accumulating the terms, we can calculate the sum efficiently.

Step-by-Step Solution

1. Input the values of the first term 'a', the common ratio 'r', and the number of terms 'n' for which we want to find the sum.

2. Initialize a variable 'sum' to 0.

3. Iterate 'n' times: a. Multiply the first term 'a' by the common ratio 'r' raised to the power of the current iteration. b. Add the result to the 'sum' variable.

4. The value of 'sum' after the loop will be the sum of terms in the Geometric Progression.

Code

Here's an example implementation for finding the sum of terms in a Geometric Progression using iteration: