Nth Term 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 Nth term in a Geometric Progression. We will cover the understanding of Geometric Progression, the approach to finding the Nth term, 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 Nth term 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) N-1 times to obtain the Nth term. By iteratively applying the common ratio, we can calculate the desired term efficiently.


Step-by-Step Solution


Code

Here's an example implementation for finding the Nth term in a Geometric Progression using iteration:

Conclusion

By using an iterative approach, we can efficiently find the Nth term in a Geometric Progression. The code provided demonstrates a simple implementation in Java, allowing you to input the first term, the common ratio, and the value of N to calculate the desired term. Understanding this approach enables us to solve problems involving Geometric Progressions and apply them in various mathematical and computational tasks.


Exercise: 

Calculate Nth term in a GP using the formula and validate if both the approaches gives same result.